Answers posted by rvidyagovindarajan_1

0 votes

If $\overrightarrow a,\:\overrightarrow b,\:\overrightarrow c$ are any three vectors such that $\overrightarrow a\times\overrightarrow b=\overrightarrow c\:\:and\:\:\overrightarrow b\times\overrightarrow c=\overrightarrow a$, then the magnitude of $\overrightarrow b$ is?

answered Dec 5, 2013

Given: $\overrightarrow a\times\overrightarrow b=\overrightarrow c\:\:and\:\:\overrightarrow b\time...

0 votes

$|\overrightarrow a\times\overrightarrow b|^2= ?$ (which one of the following )

answered Dec 3, 2013

$|\overrightarrow a\times \overrightarrow b|^2=|\overrightarrow a|^2\:|\overrightarrow b|^2.sin^2\th...

0 votes

If vector $\overrightarrow a$ is unit vector and it makes angle $\large\frac{\pi}{4}$ with $\hat k$ and $\overrightarrow a+\hat i+\hat j$ is also a unit vector, then $\overrightarrow a=?$

answered Dec 3, 2013

Let $\overrightarrow a=\alpha \hat i+\beta \hat j+\gamma \hat k$Given: $|\overrightarrow a|=1\Right...

0 votes

If $D\:\:and\:\:E$ are mid points of the side $\overline {AB}\:\:and\:\:\overline {AC}$ of a $\Delta \:ABC$, then $\overrightarrow {BE}+\overrightarrow {DC}=?$

answered Dec 3, 2013

Let the position vectors of the points $,B,C$ be $\overrightarrow b,\overrightarrow c$ respective...

0 votes

If sum of two unit vectors is also a unit vector then the magnitude of their difference is ?

answered Dec 3, 2013

Let the given unit vectors be $\overrightarrow a\:\:and\:\: \overrightarrow b$Given: $|\overrightarr...

0 votes

If $\overrightarrow {AB}=3\hat i+\hat j-2\hat k,\:and \:\overrightarrow {AC}=-\hat i+3\hat j+4\hat k$ are two sides af the $\Delta ABC$, then the length of the median through $A$ is ?

answered Dec 1, 2013

$\overrightarrow {BC}=\overrightarrow {AC}-\overrightarrow {AB}=-4\hat i+2\hat j+6\hat k$...

0 votes

If $\overrightarrow a=\hat i+\hat j+\hat k,\:\overrightarrow b=\hat i\:\:and\:\:\overrightarrow c=x\hat i-\hat j+\hat k$, then the value of $x$ for which $\overrightarrow a\:\overrightarrow b\:and\:\overrightarrow c$ are coplanar is ?

answered Dec 1, 2013

Toolbox: If $\overrightarrow a\:\overrightarrow b,\:\overrightarrow c$ are coplanar then $...

0 votes

If $\overrightarrow a=\hat i-\hat k,\:\overrightarrow b=x\hat i+\hat j+(1-x)\hat k\:and\:\overrightarrow c=y\hat i+x\hat j+(1+x-y)\hat k$, then $[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]$ depends on?

answered Dec 1, 2013

$[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]=\left |\begin{array}{ccc}1 & 0 & ...

0 votes

The term independent of $x$ in the expansion $\bigg(\large\frac{x+1}{x^{\large\frac{2}{3}}-x^{\large\frac{1}{3}}+1}-\frac{x-1}{x-\sqrt x}\bigg)^{10}$ is ?

answered Dec 1, 2013

$x+1=(x^{\frac{1}{3}})^3+1^3$$=(x^{\frac{1}{3}}+1)$$(x^{\frac{2}{3}}-x^{\frac{1}{3}}+1)$$\therefore ...

0 votes

If $\overrightarrow a,\:\overrightarrow b,\:\overrightarrow c$ are three vectors of magnitude $3,4,5$ respectively. If each vector is $\perp$ to sum of the other two vectors then $|\overrightarrow a+\overrightarrow b+\overrightarrow c|=?$

answered Nov 30, 2013

1 vote

If the sum of two unit vectors is a unit vector, then the magnitude of their difference is ?

answered Nov 30, 2013

Let the two unit vectors be $\overrightarrow a$ and $\overrightarrow b$Given $|\overrightarrow a+\...

0 votes

If $ |\overrightarrow a+\overrightarrow b|=|\overrightarrow a|$, then the angle between $2\overrightarrow a+\overrightarrow b$ and $\overrightarrow b$ is ?

answered Nov 30, 2013

Given: $|\overrightarrow a+\overrightarrow b|=|\overrightarrow a|$$\Rightarrow\:(\overrightarrow a+...

0 votes

If $\overrightarrow a= x^2\hat i+2\hat j-2\hat k,\:\overrightarrow b=\hat i-\hat j+\hat k\;and\:\overrightarrow c=x^2\hat i+5\hat j-4\hat k$ are three vectors, then the values of $x$ for which the angle between $\overrightarrow a\:and\:\overrightarrow b$ is acute and that between $\overrightarrow b\:and\:\overrightarrow c$ is obtuse is ?

answered Nov 29, 2013

Since given that the angle between $\overrightarrow a\:and\:\overrightarrow b$ is acute and that bet...

0 votes

If $\overrightarrow a,\:\overrightarrow b\:and\:\overrightarrow c$ are non coplanar vectors and if $\overrightarrow a'=\large\frac{\overrightarrow b\times \overrightarrow c}{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]},\:\overrightarrow b'=\large\frac{\overrightarrow c\times \overrightarrow a}{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]},\:and \:\overrightarrow c'=\large\frac{\overrightarrow a\times \overrightarrow b}{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]},$ then $\overrightarrow a.\overrightarrow a'+\overrightarrow b.\overrightarrow b'+\overrightarrow c.\overrightarrow c'=?$

answered Nov 29, 2013

$\overrightarrow a.\overrightarrow a'=\overrightarrow a.\large\frac{\overrightarrow a.(\overrightarr...

0 votes

answered Nov 29, 2013

Angle $\theta$ between $|\overrightarrow a|\overrightarrow b+|\overrightarrow b|\overrightarrow a$ ...

0 votes

If the vectors $p\hat i+\hat j+\hat k,\:\hat i+q\hat j+\hat k,\: \:and\:\:\hat i+\hat j+r\hat k$ $(p\neq q\neq r\neq 1)$ are three coplanar vectors then the value of $pqr-(p+q+r)=?$

answered Nov 29, 2013

If the given vectors are coplanar then$\left |\begin {array}{ccc} p & 1 & 1\\1 & q &...

0 votes

The value of $a$ for which the volume of the parallelopiped formed by the vectors $\hat i+a\hat j+\hat k,\:\:\hat j+a\hat k,\:\:a\hat i+\hat k$ is minimum is ?

answered Nov 28, 2013

Volume of the parallelopiped (V) $=\left |\begin {array} {ccc}1 & a & 1 \\0 & 1 & a\...

0 votes

If $\overrightarrow u=\hat i+\hat j,\:\overrightarrow v=\hat i-\hat j\:\:and\:\:\overrightarrow w=\hat i+2\hat j+3\hat k$. and if $\hat n$ is a unit vector such that $\overrightarrow u.\hat n=\overrightarrow v.\hat n=0$, then $|\overrightarrow w.\hat n|=?$

answered Nov 28, 2013

Let $\hat n=x\hat i+y\hat j+z\hat k$Given: $\overrightarrow u.\hat n=\overrightarrow v.\hat n=0$$\...

0 votes

If in the expansion of $(x+a)^{15},$ the $11^{th}$ term is $G.M.$ of $8^{th} $ & $12^{th}$ terms, then which term is the greatest term?

answered Nov 24, 2013

Given: $(T_{11})^2=T_8.T_{12}$ in the expansion of $(x+a)^{15}$$\Rightarrow\:\big[^{15}C_{10}.x...

0 votes

If the sum of $5^{th}\:and\:6^{th}$ terms in the expansion of $(a-b)^n$, $n\geq5$, is 0, then $\large\frac{a}{b}$ = ?

answered Nov 24, 2013

Given: $T_5+T_6=0$ in the expansion of $(a-b)^n$$\Rightarrow\:^nC_4.a^{n-4}.(-b)^4+^nC_5.a^{n-5}....

0 votes

If the sum of the coefficients of $(1+x)^n=4096$, then the largest coefficient is ?

answered Nov 24, 2013

Toolbox:Then highest coeff. out of $^{2n}C_0,^{2n}C_2,.......^{2n}C_{2n}$ is $^{2n}C_n$$^nC_0+...

0 votes

The value of $^nC_0.^{2n}C_r$ - $^nC_1^{2-2}C_r$ + $^nC_2.^{2n-4}C_r$ - ...., if $r \lt n$ is

answered Nov 24, 2013

$\big[(1+x)^2-1\big]^n=^nC_0.(1+x)^{2n}-^nC_1.(1+x)^{2n-2}+^nC_2.(1+x)^{2n-4}-.............$ ...

0 votes

Coeff. of $x^{50}$ in $(1+x)^{1000}$ + $x(1+x)^{999}$ + $x^2(1+x)^{998}$ + .... + $x^{1000}$ is

answered Nov 23, 2013

$(1+x)^{1000}+x(1+x)^{999}+x^2(1+x)^{998}+......x^{1000}$ is a G.P.$\therefore $ Sum of $1000 $ ...

0 votes

In how many ways can a mixed doubles game in tennis can be arranged from 5 couples, if no husband and wife play in the same game?

answered Nov 23, 2013

For a mixed doubles game 2 husbands and 2 wives are to be selected.First of all 2 husbands can be se...

0 votes

If $\overrightarrow u,\overrightarrow v,\overrightarrow w$ are non coplanar vectors and $p,q$ are real numbers so that $[3\overrightarrow u\:p\overrightarrow v\:p\overrightarrow w]-[p\overrightarrow v\:p\overrightarrow w\:q\overrightarrow u]-[2\overrightarrow w\:q\overrightarrow v\:q\overrightarrow u]=0$ then number of values of $p,q$ is

answered Nov 23, 2013

Toolbox:$[\overrightarrow u\:\overrightarrow v\:\overrightarrow w]=[\overrightarrow v\:\overrightarr...

0 votes

$53^{53} - 33^{33}$ is divisible by

answered Nov 22, 2013

$53^{53}-33^{33}=(33+20)^{53}-33^{33}$$=\big[^{53}C_0 .33^{53}+^{53}C_1. 33^{52}.20+^{53}C_2 33^{51}...

0 votes

If $\overrightarrow a.\overrightarrow b=\overrightarrow a.\overrightarrow c$ and $\overrightarrow a\times\overrightarrow b=\overrightarrow a\times\overrightarrow c$ and if $\overrightarrow a\neq 0$, then

answered Nov 21, 2013

Given :$\overrightarrow a.\overrightarrow b=\overrightarrow a.\overrightarrow c$ and $\overrightar...

0 votes

If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are three non coplanar vectors then $(\overrightarrow a+\overrightarrow b+\overrightarrow c).(\overrightarrow b+\overrightarrow c)\times (\overrightarrow c+\overrightarrow a)=?$

answered Nov 21, 2013

$(\overrightarrow a+\overrightarrow b+\overrightarrow c).(\overrightarrow b+\overrightarrow c)\times...

0 votes

If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are three non coplanar vectors, then $[\overrightarrow a+\overrightarrow b+\overrightarrow c\:\overrightarrow a-\overrightarrow c\:\overrightarrow a-\overrightarrow b]=?$

answered Nov 21, 2013

$[\overrightarrow a+\overrightarrow b+\overrightarrow c\:\overrightarrow a-\overrightarrow c\:\overr...

0 votes

If $\overrightarrow a\:\:and\:\:\overrightarrow b$ are two non zero non collinear vectors, then $[\overrightarrow a\:\overrightarrow b\:\hat i]\hat i+[\overrightarrow a\:\overrightarrow b\:\hat j]\hat j+[\overrightarrow a\:\overrightarrow b\:\hat k]\hat k=?$

answered Nov 20, 2013

Toolbox:$(\overrightarrow a.\hat i)\hat i+(\overrightarrow a.\hat j)\hat j+(\overrightarrow a.\hat k...

0 votes

If $\overrightarrow a=\hat i+\hat j,\:\:\overrightarrow b=2\hat j-\hat k$ and $\overrightarrow r\times \overrightarrow a=\overrightarrow b\times\overrightarrow a,\:\:\overrightarrow r\times\overrightarrow b=\overrightarrow a\times\overrightarrow b$ then a unit vector in the direction of $\overrightarrow r$ is ?

answered Nov 20, 2013

Given: $\overrightarrow r \times\overrightarrow b=\overrightarrow a\times\overrightarrow b\:\:and\:...

0 votes

If $\overrightarrow a\:\:and\:\:\overrightarrow b$ are unit non collinear vectors and if $\overrightarrow u=\overrightarrow a-(\overrightarrow a.\overrightarrow b)\overrightarrow b$ and $\overrightarrow v=\overrightarrow a\times\overrightarrow b$ then $ |\overrightarrow v|= ?$

answered Nov 20, 2013

Toolbox:$\overrightarrow a\times (\overrightarrow b\times\overrightarrow c)=(\overrightarrow a.\over...

0 votes

If $\overrightarrow a=2\hat i+\hat j-2\hat k\:\:and\:\:\overrightarrow b=\hat i+\hat j.$ and $\overrightarrow c$ is a vector such that $\overrightarrow a.\overrightarrow c=|\overrightarrow c|,\:\:|\overrightarrow c-\overrightarrow a|=2\sqrt 2 $ and angle between $\overrightarrow a\times\overrightarrow b\:\:and\:\:\overrightarrow c$ is $\large\frac{\pi}{6}$, then $|(\overrightarrow a\times\overrightarrow b)\times\overrightarrow c|=?$

answered Nov 20, 2013

Given: $\overrightarrow a.\overrightarrow c=|\overrightarrow c|\:\:and\:\:|\overrightarrow c-\over...

0 votes

If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are non zero, non collinear vectors such that $\overrightarrow a\times\overrightarrow b=\overrightarrow b\times\overrightarrow c=\overrightarrow c\times\overrightarrow a$, then $\overrightarrow a+\overrightarrow b+\overrightarrow c=?$

answered Nov 20, 2013

Given: $\overrightarrow a\times\overrightarrow b=\overrightarrow b\times\overrightarrow c$$\Rightar...

0 votes

If the magnitude of the vector $a\hat i+b\hat j+c\hat k$ is $|a|+|b|+|c|$, then $a,b,c$ should be ?

answered Nov 19, 2013

Given: $ \sqrt {a^2+b^2+c^2}=|a|+|b|+|c|$$\Rightarrow\:a^2+b^2+c^2=a^2+b^2+c^2+2(|a||b|+|b||c|+|c||...

0 votes

If $\overrightarrow a\:and\:\overrightarrow c$ are unit and collinear vectors and $|\overrightarrow b|=6$, then $\overrightarrow b-3\overrightarrow c=\lambda \overrightarrow a,$ if $\lambda=?$

answered Nov 19, 2013

Given: $\overrightarrow b-3\overrightarrow c=\lambda \overrightarrow a$$\Rightarrow\:(\overrightarr...

0 votes

If $|\overrightarrow a|=|\overrightarrow b|=1$ and $|\overrightarrow a+\overrightarrow b|=\sqrt 3$ and $\overrightarrow c$ is such that $\overrightarrow c-\overrightarrow a-2\overrightarrow b=3(\overrightarrow a\times\overrightarrow b)$, then $\overrightarrow c.\overrightarrow b=?$

answered Nov 19, 2013

0 votes

If $|\overrightarrow a|=5, \:|\overrightarrow b|=3\:|\overrightarrow c|=4$ and $\overrightarrow a$ is $\perp$ to $\overrightarrow b\:\:and\:\:\overrightarrow c$ then $[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]=?$

answered Nov 18, 2013

Given: $\overrightarrow a$ is $\perp$ to $\overrightarrow b\:\:and\:\:\overrightarrow c$$\Righta...

0 votes

If $\overrightarrow u,\overrightarrow v,\overrightarrow w$ are three vectors such that $|\overrightarrow u|=1,\:|\overrightarrow v|=2,\:|\overrightarrow w|=3$ and if the projection of $\overrightarrow v$ along $\overrightarrow u$ is equal to that of $\overrightarrow w$ along $\overrightarrow u$ and also if $\overrightarrow u$ and $\overrightarrow v$ are $\perp$ to each other, then $ |\overrightarrow u-\overrightarrow v+\overrightarrow w|= ?$

answered Nov 18, 2013

Given: Projection of $\overrightarrow v$ along $\overrightarrow u$ = Projection of $\overrighta...

0 votes

The value of $[\overrightarrow a-\overrightarrow b\:\:\overrightarrow b-\overrightarrow c\:\:\overrightarrow c-\overrightarrow a]$ where $|\overrightarrow a|=1,\:\:|\overrightarrow b|=5\:\:|\overrightarrow c|=3$ is ?

answered Nov 18, 2013

$[\overrightarrow a-\overrightarrow b\:\:\overrightarrow b-\overrightarrow c\:\:\overrightarrow c-\o...

0 votes

The greatest value of $|\overrightarrow a+\overrightarrow b|+|\overrightarrow a-\overrightarrow b|$ where $\overrightarrow a\:\:and\:\:\overrightarrow b$ are unit vectors is ?

answered Nov 18, 2013

Toolbox:Max. value of $acos\theta+bsin\theta= \sqrt {a^2+b^2}$$|\overrightarrow a+\overrigh...

0 votes

If $\overrightarrow a=2\hat i+3\hat j-\hat k\:\:and\:\:\overrightarrow b=\hat i-2\hat j+3\hat k$, then the value of $\lambda$ for which $\overrightarrow c=\lambda\hat i+\hat j+(2\lambda+1)\hat k$ is parallel to the plane containing $\overrightarrow a\:\:and\:\:\overrightarrow b$ is

answered Nov 15, 2013

Given that $\overrightarrow c$ is parallel to the plane containing $\overrightarrow a\:and\:\overri...

0 votes

If $\overrightarrow a,\overrightarrow b\:\overrightarrow c$ are three vectors of equal magnitude and angle between $\overrightarrow a\:and\:\overrightarrow b$ is $\alpha$, that between $\overrightarrow b\:\overrightarrow c$ is $\beta$, and that between $\overrightarrow a\:and\:\overrightarrow c$ is $\gamma$ then the minimum value of $cos\alpha+cos\beta+cos\gamma$ is ?

answered Nov 15, 2013

0 votes

If $\overrightarrow {OA}=\hat i+3\hat j-2\hat k\:\:and\:\:\overrightarrow {OB}=3\hat i+\hat j-2\hat k$ and $\overrightarrow {OC} $ is angular bisector of angle $AOB$ with $C$ being the point on the line $AB$, then $\overrightarrow {OC}=?$

answered Nov 13, 2013

Since $ |\overrightarrow {OA}|=|\overrightarrow {OB}=\sqrt {14}$$\Delta AOB$ is isosceles triangle...

0 votes

If $a,b,c$ are lengths of sides of a $\Delta\:ABC$ and for any non collinear vectors $\overrightarrow u\:\:and\:\:\overrightarrow v$ if $(a-b)\overrightarrow u+(b-c)\overrightarrow v+(c-a)(\overrightarrow u\times\overrightarrow v)=0$, then the $\Delta$ is ?

answered Nov 13, 2013

Toolbox:If three vectors $\overrightarrow x,\:\overrightarrow y,\:\overrightarrow z$ are non coplana...

0 votes

find the equation of plane through (-1,2,1) and perpendicular to the line joining (-3,1,2) and (2,3,4) find the distance of plane from origin

answered Nov 13, 2013

Let the equation of the plane be $ax+by+cz+d=0$$\Rightarrow\: $ D.R. of normal to the plane is $(a...

0 votes

find equation of plane containing (1,2,3) and perpendicular to the place 3x- y +2z= 3 and parallel to the line x-1/3=y/2=z/-2.write equation in dot product form

answered Nov 13, 2013

Let the equation of the plane be $ax+by+cz+d=0$ $\Rightarrow\:$ D.R. of the normal to the p...

0 votes

If $\overrightarrow a=\hat i+\hat j+\hat k\:\:\overrightarrow b=4\hat i+3\hat j+4\hat k\:\:and\:\:\overrightarrow c=\hat i+\alpha\hat j+\beta\hat k$ are linear dependent vectors and $|\overrightarrow c|=\sqrt 3$ then $ (\alpha,\beta)=?$

answered Nov 12, 2013

Toolbox:If $\overrightarrow a, \:\overrightarrow b\:\;and\:\:\overrightarrow c$ are linearly depen...

0 votes

The value of $a$ for which the volume of the parallelopiped formed by vectors $\hat i+a\hat j+\hat k,\:\:\hat j+a\hat k\:\:and\:\: a\hat i+\hat k$ becomes minimum is ?

answered Nov 12, 2013

Volume of a parallelopiped = $\left|\begin {array}{ccc}1 &a & 1\\0 &1 &a\\a & 0 ...

0 votes

If $ \overrightarrow x=\large\frac{\overrightarrow b\times\overrightarrow c}{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]},\:\:\overrightarrow y=\large\frac{\overrightarrow c\times\overrightarrow a}{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]},\:\:and\:\:\overrightarrow z=\large\frac{\overrightarrow a\times\overrightarrow b}{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]},$ then $\overrightarrow x.(\overrightarrow a+\overrightarrow b)+\overrightarrow y.(\overrightarrow b+\overrightarrow c)+\overrightarrow z.(\overrightarrow c+\overrightarrow a)=?$

answered Nov 12, 2013

$\overrightarrow x.(\overrightarrow a+\overrightarrow b)=\large\frac{\overrightarrow b\times\overrig...

Ask Questions, Get Answers