Recent questions tagged ch10

The length of perpendicular from the origin to a line is 6 and line makes an angle of $145^{\large\circ}$ with the positive direction of y-axis .Find the equation of line.

asked Feb 4, 2014 by sreemathi.v

1 answer

Find the equation of straight line passing through $(at_1,\large\frac{a}{t_1})$ & $(at_2,\large\frac{a}{t_2})$?

asked Feb 4, 2014 by sreemathi.v

1 answer

Find the equations of the bisectors of the angle between the co-ordinate axes?

asked Feb 4, 2014 by sreemathi.v

1 answer

Find the value of $m$ and $c$ if the straight line ( equation is $y=mx +c$ ) passes through the point $A(2,3)$ and $B(1,6)$.

asked Feb 4, 2014 by sreemathi.v

1 answer

Find the equation of a line which is equidistant from the line $x=\large\frac{15}{2}$ and $x=\large\frac{1}{2}$?

asked Feb 4, 2014 by sreemathi.v

1 answer

Find $|\overrightarrow x|$, if for a unit vector $\overrightarrow a,\:(\overrightarrow x-\overrightarrow a).(\overrightarrow x+\overrightarrow a)=15$

asked Feb 3, 2014 by rvidyagovindarajan_1

1 answer

A line passes through the points $A(1,2)$ and $B(4,+2)$.Find the slope of the line parallel to AB ?

asked Feb 3, 2014 by sreemathi.v

1 answer

Find the angle between the lines whose slope are $\large\frac{3}{2}$ and 7?

asked Feb 3, 2014 by sreemathi.v

1 answer

Determine the value of $\lambda$ so that 1 is the slope of line passing through (1,1) and $(\lambda,4)$?

asked Feb 3, 2014 by sreemathi.v

1 answer

Find the inclination of the line whose slope is 1?

asked Feb 3, 2014 by sreemathi.v

1 answer

If the sum of two unit vector is a unit vector, then what is the angle between them?

asked Feb 3, 2014 by rvidyagovindarajan_1

1 answer

What is the angle between following planes $2x-3y+4z=1$ and $-x+y=4$?

asked Jan 30, 2014 by balaji

1 answer

What is the area of the parallelogram having diagonals $ 3\bar{i}+\bar{j}-2\bar{k}\;and\;\bar{i}-3\bar{j}+4\bar{k}$?

asked Jan 30, 2014 by balaji

1 answer

The volume of a parallelopiped formed by $\hat i+a\hat j+\hat k,\:\hat j+a\hat k\:and\:\:a\hat i+\hat k$ is minimum if $a=?$

asked Jan 13, 2014 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 $\overrightarrow n$ is a unit vector such that $\overrightarrow n.\overrightarrow u=\overrightarrow n.\overrightarrow v=0$, then $|\overrightarrow n.\overrightarrow w|=?$

asked Jan 13, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow v=2\hat i+\hat j-\hat k\:\:and\:\;\overrightarrow w=\hat i+3\hat k$ and $\overrightarrow u$ is a unit vector,then the maximum value of $ [\overrightarrow u\:\overrightarrow v\:\overrightarrow w]$ is ?

asked Jan 13, 2014 by rvidyagovindarajan_1

1 answer

If $ \overrightarrow r\times\overrightarrow b=\overrightarrow c\times\overrightarrow b$ and $\overrightarrow r.\overrightarrow a=0$, where $\overrightarrow a=2\hat i+3\hat j-\hat k,\:\overrightarrow b=3\hat i-\hat i+\hat k\:and\:\:\overrightarrow c=\hat i+\hat j+3\hat k$, then $\overrightarrow r=?$

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=(-1,1,1)\:\:\overrightarrow b=(2,0,1)\:and\:\overrightarrow x$ is vector such that $\overrightarrow x.\overrightarrow a=7,\:\overrightarrow x.\overrightarrow b=0$ and $\overrightarrow a,\overrightarrow b,\overrightarrow x$ are coplanar, then $\overrightarrow x=?$

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

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 $P$ is point whose position vector is $\overrightarrow r=x\hat i+y\hat j+z\hat k$ where $x,y,z \in N$ and $\overrightarrow a=\hat i+\hat j+\hat k$, then the number of possible points $P$ for which $\overrightarrow r.\overrightarrow a=10$ is ?

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=\hat i+\hat j+\hat k,\:\:\overrightarrow c=\hat j-\hat k$ and $\overrightarrow b$ is such that $\overrightarrow a\times\overrightarrow b=\overrightarrow c\:\:and\:\:\overrightarrow a.\overrightarrow b=3$ then $\overrightarrow b=?$

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=2\hat i+\hat j-2\hat k\:\;and\:\:\overrightarrow b=\hat i+\hat j$ and $\overrightarrow c$ is such that $\overrightarrow c.\overrightarrow a=|\overrightarrow c|$, $|\overrightarrow c-\overrightarrow a|=2\sqrt 2$ and the angle between $\overrightarrow a\times\overrightarrow b$ and $\overrightarrow c$ is $30^{\circ}$, then $|(\overrightarrow a\times\overrightarrow b)\times\overrightarrow c|=?$

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\overrightarrow b$ are mutually $\perp$ unit vectors and the vectors $x\overrightarrow a+x\overrightarrow b+z(\overrightarrow a\times\overrightarrow b ),\:\:\overrightarrow a+(\overrightarrow a\times\overrightarrow b),\:\:and\:\:z\overrightarrow a+z\overrightarrow b+y(\overrightarrow a\times\overrightarrow b)$ lie in a plane then $Z$ is ?

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are unit vectors and $\overrightarrow a+\overrightarrow b+\overrightarrow c$ is also a unit vector and $\alpha,\beta,\gamma $ are angles between $\overrightarrow a\:and\:\overrightarrow b,\:\:\overrightarrow b\:and\:\overrightarrow c\:\:\overrightarrow c\:and\:\overrightarrow a$ respectively, then among the three angles,

asked Jan 6, 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

If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are three coplanar vectors then, $[(2\overrightarrow a-\overrightarrow b)\:(2\overrightarrow b-\overrightarrow c)\:(2\overrightarrow c-\overrightarrow a)]=?$

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

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

asked Dec 17, 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