Recent questions in Class12

Evaluate : $\begin{vmatrix}0 &a-b&b-c\\b-a&0&b-c\\c-a&c-b&0\end{vmatrix}$

asked Nov 19, 2013 by sreemathi.v

1 answer

Evaluate : $\begin{vmatrix}1&\omega&\omega^2\\\omega&\omega^2&1\\\omega^2&1&\omega\end{vmatrix}$

( $\omega$ : Cube root of unity)

asked Nov 19, 2013 by sreemathi.v

1 answer

Evaluate : $\begin{vmatrix}3 &2& 12\\0 &1&8\\2&9&7\end{vmatrix}$

asked Nov 19, 2013 by sreemathi.v

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 $\overrightarrow a=2\hat i+3\hat j-\hat k\:\:and\:\:\overrightarrow b=\hat i-2\hat j+3\hat k$ , 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

asked Nov 15, 2013 by rvidyagovindarajan_1

1 answer

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 ?

asked Nov 15, 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 $a,b,c$ 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 ?

asked Nov 13, 2013 by rvidyagovindarajan_1

1 answer

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 $(\alpha,\beta)=?$

asked Nov 12, 2013 by rvidyagovindarajan_1

1 answer

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 ?

asked Nov 12, 2013 by rvidyagovindarajan_1

1 answer

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 $\overrightarrow x.(\overrightarrow a+\overrightarrow b)+\overrightarrow y.(\overrightarrow b+\overrightarrow c)+\overrightarrow z.(\overrightarrow c+\overrightarrow a)=?$

asked Nov 12, 2013 by rvidyagovindarajan_1

1 answer

For non zero vectors $\overrightarrow a,\overrightarrow b\:and\:\overrightarrow c,\:\:if\:\:|(\overrightarrow a\times\overrightarrow b).\overrightarrow c|=|\overrightarrow a||\overrightarrow b||\overrightarrow c|$ then ?

asked Nov 11, 2013 by rvidyagovindarajan_1

1 answer

If $a,b,c$ are non negative and distinct numbers and vectors $a\hat i+a\hat j+c\hat k,\:\:\hat i+\hat k\:\:and\:\:c\hat i+c\hat j+b\hat k$ lie in a plane then c is ?

asked Nov 11, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=\hat i+\hat j+\hat k,\:\:\overrightarrow a.\overrightarrow b=1$ and $\overrightarrow a\times\overrightarrow b=\hat j-\hat k,$ then $\overrightarrow b=?$

asked Nov 10, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\overrightarrow b\:\:and\:\:\overrightarrow c$ are non coplanar vectors, then for real $\lambda$ , $[\lambda(\overrightarrow a+\overrightarrow b)\:\lambda^2\overrightarrow b\:\lambda\overrightarrow c]=[\overrightarrow a\:\overrightarrow b+\overrightarrow c\:\overrightarrow c]$ , for:

asked Nov 10, 2013 by rvidyagovindarajan_1

1 answer

For any vector $\overrightarrow a$ the value of $(\overrightarrow a\times \hat i)^2+(\overrightarrow a\times \hat j)^2+(\overrightarrow a\times \hat i)^2=?$

asked Nov 10, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=\hat i+2\hat j+\hat k,\:\overrightarrow b=\hat i-\hat j+\hat k$ and $\overrightarrow c=\hat i+\hat j-\hat k$ and a vector $\overrightarrow d$ which is in the plane of $\overrightarrow a\:and\:\overrightarrow b$ and whose projection on $\overrightarrow c$ is $\large\frac{1}{\sqrt 3},$ then $\overrightarrow d=?$

asked Nov 10, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a, \:\overrightarrow b,\: \overrightarrow c$ are position vectors of the points $A,B,C$ respectively, then under what condition the three points $A,B,C$ are collinear?

asked Nov 10, 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

If $\overrightarrow {OA}=\overrightarrow a,\:\overrightarrow {AB}=6\overrightarrow a+2\overrightarrow b\:and\:\overrightarrow {OC}=\overrightarrow b$ , $p$ is area of quadrateral $OACB$ and $q$ is area of parallelogram with $OA$ and $OC$ as adjacent sides, and if $p=x.q$ , then $x=?$

asked Nov 8, 2013 by rvidyagovindarajan_1

1 answer

The vector that makes equal angle with $\large\frac{1}{3}$ $(\hat i-2\hat j+2\hat k), \:\large\frac{1}{5}$ $(-4\hat i-3\hat k)$ and $\hat j$ is ?

asked Nov 7, 2013 by rvidyagovindarajan_1

1 answer

The set of all possible values of $'c'$ for which $\overrightarrow a=c \log_3 x\hat i-6\hat j+3\hat k$ and $\overrightarrow b=\log_3x\hat i+2\hat j+2c\log_3x\hat k$ making acute angle for $\forall x\in (0,\infty)$ is ?

asked Nov 6, 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

Area of a parallelogram with adjacent sides $\overrightarrow a=\overrightarrow p+2\overrightarrow q,$ and $\overrightarrow b=2\overrightarrow p+\overrightarrow q$ , where $\overrightarrow p,\overrightarrow q$ are unit vectors with angle $\large\frac{\pi}{6}$ between them is ?

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