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Recent questions tagged addition-of-vectors

In a rt. angled triangle $ABC$ if hypotenuse, $AB=p$, then $\overrightarrow {AB}.\overrightarrow {AC}+\overrightarrow {BC}.\overrightarrow {BA}+\overrightarrow {CA}.\overrightarrow {CB}$= ?

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

A vector $a\hat i+b\hat j+c\hat k$ is such that its magnitude is $ |a|+|b|+|c|$. This is possible only if

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are any three vectors such that $\overrightarrow a=\overrightarrow b+\overrightarrow c$ and $\overrightarrow b$ is $\perp$ to $\overrightarrow c$, then ?

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

If the vectors $\overrightarrow a+\lambda \overrightarrow b+3\overrightarrow c,\:-2\overrightarrow a+3\overrightarrow b-4\overrightarrow c\:and\:\overrightarrow a-3\overrightarrow b+5\overrightarrow c$ are coplanar and $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are non coplanar, then $\lambda=?$

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are the sides $BC,CA\:and \:AB$ respectively of the $\Delta \:ABC$, then

asked Jan 5, 2014 by rvidyagovindarajan_1

1 answer

The position vector of the vertices $A,B,C$ of a $\Delta\: ABC$ are $\hat i-\hat j-3\hat k,\:2\hat i+\hat j-2\hat k\:\:and\:\:-5\hat i+2\hat j-6\hat k$ respectively. The length of the bisector $AD$ of angle $A$ where $D$ is on the line $BC$ is ?

asked Jan 5, 2014 by rvidyagovindarajan_1

1 answer

A unit vector coplanar with the vectors $\hat i-\hat j\:\;and\:\:\hat i+2\hat j$ and is $\perp$ to the first vector, $\hat i-\hat j$ is ?

asked Jan 5, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow {OA}=\hat i+3\hat j-2\hat k\:\:and\:\:\overrightarrow {OB}=3\hat i+\hat j-2\hat k$ and $C$ is a point of $AB$ so that $\overrightarrow {OC}$ bisects the angle $AOB$, then $\overrightarrow {OC}=?$

asked Jan 5, 2014 by rvidyagovindarajan_1

1 answer

If position vector of the points $A,B,C,D$ are given by $7\hat i-4\hat j+7\hat k,\:\hat i-6\hat j+10\hat k,\:-\hat i-3\hat j+4\hat k\:\:and\:\:5\hat i-\hat j+5\hat k$ respectively, then $ABCD$ is ?

asked Dec 30, 2013 by rvidyagovindarajan_1

1 answer

The length of median through $A$ of the $\Delta\:ABC$ where $\overrightarrow {AB}=3\hat i+4\hat k\:\:and\:\:\overrightarrow {AC}=5\hat i-2\hat j+4\hat k$ is ?

asked Dec 30, 2013 by rvidyagovindarajan_1

1 answer

The vector $\overrightarrow a=\alpha\hat i+2\hat j+\beta\hat k$ lies in the plane of the vectors $\overrightarrow b=\hat i+\hat j$ and $\overrightarrow c=\hat j+\hat k$ and bisects the angle between $\overrightarrow b\:\:and\:\:\overrightarrow c$, then $(\alpha,\beta)=?$

asked Dec 29, 2013 by rvidyagovindarajan_1

1 answer

A parallelogram has adjacent sides $\overrightarrow a=3\overrightarrow p-\overrightarrow q\:\;and\:\:\overrightarrow b=\overrightarrow p+3\overrightarrow q$ where $ |\overrightarrow p|=|\overrightarrow q|=2$, and the angle between $\overrightarrow p\:\:and\:\:\overrightarrow q$ is $\large\frac{\pi}{3}$. The length of its diagonals are?

asked Dec 13, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=\hat i+\hat j+p\hat k\:\:and\:\:\overrightarrow b=\hat i+\hat j+\hat k$, then $|\overrightarrow a+\overrightarrow b|=|\overrightarrow a|+|\overrightarrow b|$ holds for ?

asked Dec 10, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow {\alpha}=(x+4y)\overrightarrow a+(2x+y+1)\overrightarrow b\:\:and\:\:\overrightarrow {\beta}=(y-2x+2)\overrightarrow a+(2x-3y-1)\overrightarrow b$ where $\overrightarrow a\:\:\overrightarrow b$ are non zero non collinear and if $3\overrightarrow {\alpha}=2\overrightarrow {\beta}$, then $(x,y)=?$

asked Dec 10, 2013 by rvidyagovindarajan_1

1 answer

If a person standing at the point $(1,2) $ walks $5$ units towards east, then $3$ units towards north and $\sqrt 2$ units along the direction of $\hat i+\hat j$ and then walks $\sqrt 2 $ unit along the direction $\perp$ to this vector towards the starting point. What is the displacement of the person from origin?

asked Dec 9, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a+2\overrightarrow b+3\overrightarrow c=\overrightarrow 0$, then $\overrightarrow a\times\overrightarrow b+\overrightarrow b\times\overrightarrow c+\overrightarrow c\times\overrightarrow a=?$

asked Dec 8, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=2p\hat i+\hat j$ is rotated about an angle of $\theta$ in anti clock wise direction and becomes $(p+1)\hat i+\hat j$

asked Dec 8, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a\:\:and\:\:\overrightarrow b$ are unit vectors that are inclined at angle $2\theta$ where $0\leq \theta \leq \pi$ and $|\overrightarrow a-\overrightarrow b| < 1$ then $ \theta$ lies in the interval....

asked Dec 8, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow b\:\:is\:\: \perp\:\:to \:\:\overrightarrow a+\overrightarrow b\:\:and\:\:\overrightarrow a\:\:is\:\:\perp \:\:to\:\:2\overrightarrow b+\overrightarrow a$ then $|\overrightarrow a|=?$

asked Dec 8, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a\:\:and\:\:\overrightarrow b$ are two unit vectors such that $\overrightarrow a+2\overrightarrow b\:\:and\:\:5\overrightarrow a-4\overrightarrow b$ are $\perp$ to each other, then the angle between $\overrightarrow a\:\:and\:\:\overrightarrow b$ is?

asked Dec 8, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\:\overrightarrow b,\:\overrightarrow c$ are unit vectors, then the maximum value of $|\overrightarrow a-\overrightarrow b|^2+|\overrightarrow b-\overrightarrow c|^2+|\overrightarrow c-\overrightarrow a|^2$ is ?

asked Dec 7, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a\times\overrightarrow b+\overrightarrow b\times\overrightarrow c+\overrightarrow c\times\overrightarrow a$ and $\overrightarrow a+\overrightarrow b+\overrightarrow c$ are $\perp$ then $\overrightarrow a,\:\overrightarrow b\:\overrightarrow c$ are .....

asked Dec 7, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a$ is any vector such that $\overrightarrow a\times \hat i+2\overrightarrow a-5\hat k=\overrightarrow 0$, then $\overrightarrow a=?$

asked Dec 6, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow d=x(\overrightarrow a \times\overrightarrow b)+y(\overrightarrow b\times\overrightarrow c)+z(\overrightarrow c\times\overrightarrow a)$ and $[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]=\large\frac{1}{8}$, then $x+y+z=?$

asked Dec 6, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=p\hat i+3\hat j+4\hat k\:\:and\:\:\overrightarrow b=\sqrt q\hat i+5\hat k$ are two vectors of same magnitude, then no. of values of $(p,q)$ are?

asked Dec 6, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=\hat i+\hat j-\hat k,\:\overrightarrow b=-\hat i+2\hat j+\hat k\:\:and\:\:\overrightarrow c=-\hat i+2\hat j-\hat k$, then a unit vector $\perp$ to $\overrightarrow a+\overrightarrow b$ and $\overrightarrow b+\overrightarrow c$ is ?

asked Dec 6, 2013 by rvidyagovindarajan_1

1 answer

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 $\overrightarrow a=?$

asked Dec 3, 2013 by rvidyagovindarajan_1

1 answer

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

asked Dec 3, 2013 by rvidyagovindarajan_1

1 answer

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

asked Dec 3, 2013 by rvidyagovindarajan_1

1 answer

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 $|\overrightarrow a+\overrightarrow b+\overrightarrow c|=?$

asked Nov 30, 2013 by rvidyagovindarajan_1

1 answer

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

asked Nov 30, 2013 by rvidyagovindarajan_1

1 answer

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

asked Nov 29, 2013 by rvidyagovindarajan_1

1 answer

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 $pqr-(p+q+r)=?$

asked Nov 29, 2013 by rvidyagovindarajan_1

1 answer

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 $|\overrightarrow w.\hat n|=?$

asked Nov 28, 2013 by rvidyagovindarajan_1

1 answer

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

asked Nov 21, 2013 by rvidyagovindarajan_1

1 answer

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

asked Nov 21, 2013 by rvidyagovindarajan_1

1 answer

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 $\overrightarrow a+\overrightarrow b+\overrightarrow c=?$

asked Nov 19, 2013 by rvidyagovindarajan_1

1 answer

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 ?

asked Nov 19, 2013 by rvidyagovindarajan_1

1 answer

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 $\overrightarrow c.\overrightarrow b=?$

asked Nov 19, 2013 by rvidyagovindarajan_1

1 answer

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

asked Nov 18, 2013 by rvidyagovindarajan_1

1 answer

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|= ?$

asked Nov 18, 2013 by rvidyagovindarajan_1

1 answer

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 ?

asked Nov 18, 2013 by rvidyagovindarajan_1

1 answer

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

asked Nov 18, 2013 by rvidyagovindarajan_1

1 answer

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 $\overrightarrow {OC}=?$

asked Nov 13, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\overrightarrow b\:and\:\overrightarrow c$ are non zero vectors that are pair wise non-collinear and if $\overrightarrow a+3\overrightarrow b$ is collinear with $ \overrightarrow c$ and $\overrightarrow b+2\overrightarrow c $ is collinear with $\overrightarrow a$, then $\overrightarrow a+3\overrightarrow b+6\overrightarrow c=?$

asked Nov 9, 2013 by rvidyagovindarajan_1

1 answer

If $|\overrightarrow a+\overrightarrow b|=\sqrt {29}$ and $\overrightarrow a\times (2\hat i+3\hat j+4\hat k)=(2\hat i+3\hat j+4\hat k)\times \overrightarrow b,$ then $(\overrightarrow a+\overrightarrow b).(-7\hat i+2\hat j+3\hat k)=?$

asked Nov 9, 2013 by rvidyagovindarajan_1

1 answer

If $|\overrightarrow a|=3,\:|\overrightarrow b|=\large\frac{\sqrt 2}{3}$, then $\overrightarrow a\times\overrightarrow b$ is a unit vector if the angle between $\overrightarrow a$ and $\overrightarrow b$ is ?

asked Nov 8, 2013 by rvidyagovindarajan_1

1 answer

The number of distinct real values of $\lambda$ for which the vectors $-\lambda^2\hat i+\hat j+\hat k,\:\hat i-\lambda^2\hat j+\hat k\:and\:\hat i+\hat k-\lambda^2 \hat k$ are coplanar is?

asked Nov 8, 2013 by rvidyagovindarajan_1

1 answer

In a rt. angled $\Delta$ $ABC$, the hypotenuse $|\overrightarrow {AB}|=p$,then $\overrightarrow {AB}.\overrightarrow {AC}+\overrightarrow {BC}.\overrightarrow {BA}+\overrightarrow {CA}.\overrightarrow {CB}=?$

asked Nov 6, 2013 by rvidyagovindarajan_1

1 answer

$|\overrightarrow a|=3,\:|\overrightarrow b|=4,\:|\overrightarrow a+\overrightarrow b|=5,$ then $|\overrightarrow a-\overrightarrow b|=?$

asked Nov 6, 2013 by rvidyagovindarajan_1

1 answer

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