Recent questions tagged class12

If the projection of $\overrightarrow{a} $ on $\overrightarrow{b} $ and the projection of $\overrightarrow{b}$ on $\overrightarrow{a}$ are equal then the angle between $\overrightarrow{a}+\overrightarrow{b}$ and $\overrightarrow{a}-\overrightarrow{b}$ is

asked May 10, 2013 by poojasapani_1

1 answer

The projection of $\overrightarrow{OP}$ on a unit vector $\overrightarrow{OQ}$ equals thrice the area of parallelogram $OPRQ$. Then $\angle{POQ}$ is

asked May 10, 2013 by poojasapani_1

1 answer

The equation of the plane passing through the point $(2 , 1 , -1 )$ and the line of intersection of the planes $\overrightarrow{r}. (\overrightarrow{i}+\overrightarrow{3j}-\overrightarrow{k})=0$ and $\overrightarrow{r}. (\overrightarrow{j}+\overrightarrow{2k})=0$ is

asked May 10, 2013 by poojasapani_1

1 answer

The point of intersection of the line $\overrightarrow{r}=(\overrightarrow{i}-\overrightarrow{k}) + t(\overrightarrow{3i}+\overrightarrow{2j}+\overrightarrow{7k})$ and the plane $\overrightarrow{r}. (\overrightarrow{i}+\overrightarrow{j}-\overrightarrow{k})=8 $ is

asked May 10, 2013 by poojasapani_1

1 answer

The equation of the line parallel to $\large\frac{x-3}{1}=\frac{y+3}{5}=\frac{2z-5}{3}$ and passing through the point $(1 , 2 ,5 ) $ in vector form is

asked May 10, 2013 by poojasapani_1

1 answer

Find the coordinates of the foot of the perpendicular drawn from the origin to the plane $(d)\;5y + 8 = 0 $

asked May 9, 2013 by rvidyagovindarajan_1

1 answer

Find the coordinates of the foot of the perpendicular drawn from the origin to the plane $(c)\; x + y + z = 1 $

asked May 9, 2013 by rvidyagovindarajan_1

1 answer

Find the coordinates of the foot of the perpendicular drawn from the origin to the plane $(b)\; 3y + 4z – 6 = 0 $

asked May 9, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow{PR}=2\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}, \;\overrightarrow{QS}=-\overrightarrow{i}+\overrightarrow{3j}+\overrightarrow {2k},$ then the area of the quadrilateral $PQRS$ is

asked May 9, 2013 by poojasapani_1

0 answers

If $\overrightarrow{a}\times(\overrightarrow{b}\times \overrightarrow{c})+\overrightarrow{b} \times (\overrightarrow{c} \times \overrightarrow{a})+\overrightarrow{c} \times (\overrightarrow{a}\times \overrightarrow{b})=\overrightarrow{x}\times\overrightarrow{y} $ then

asked May 9, 2013 by poojasapani_1

1 answer

If $\overrightarrow{p} ,\overrightarrow{q}$ and $\overrightarrow{p}+\overrightarrow{q}$ are vectors of magnitude $\lambda$ than the magnitude of $|\overrightarrow{p}-\overrightarrow{q}|$ is

asked May 9, 2013 by poojasapani_1

1 answer

If $|\overrightarrow{a+b}|=|\overrightarrow{a-b}|$ then

asked May 9, 2013 by poojasapani_1

1 answer

The area of the parallelogram having a diagonal $\overrightarrow{3i}+\overrightarrow{j}-\overrightarrow{k}$ and a side $\overrightarrow{i}-\overrightarrow{3j}+\overrightarrow{4k} $ is

asked May 9, 2013 by poojasapani_1

1 answer

The vectors $\overrightarrow{2i}+\overrightarrow{3j}+\overrightarrow{4k} $ and $\overrightarrow{ai}+\overrightarrow{bj}+\overrightarrow{ck}$ are perpendicular when

asked May 9, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a}+{b}+{c}=0,|\overrightarrow{a}|=3, |\overrightarrow{b}|=4,|\overrightarrow{c}|=5$ then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is

asked May 9, 2013 by poojasapani_1

1 answer

Find the Cartesian equation of the following planes: (c) $ r .[(s - 2t)\hat i + (3- t) \hat j +(2 s + t) \hat k] = 15$

asked May 8, 2013 by rvidyagovindarajan_1

1 answer

Find the Cartesian equation of the plane $(b)\; \overrightarrow r . (2\hat i +3\hat j - 4\hat k) = 1 $

asked May 8, 2013 by rvidyagovindarajan_1

1 answer

If $A=\large\frac{1}{3}$$\begin{bmatrix} 2 & 2 & 1 \\-2 & 1 & 2 \\1 & -2 & 2 \end{bmatrix}$ prove that $A^{-1}=A^T$.

asked May 8, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a}$ and $\overrightarrow{b} $ include an angle $120^{\circ}$ and their magnitude are $2$ and $\sqrt{3}$ then $\overrightarrow{a} .\overrightarrow{b} $ is equal to

asked May 8, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two unit vectors and $\theta $is the angle between them, then $(\overrightarrow{a}+\overrightarrow{b})$ is a unit vector if

asked May 8, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a}$ is a non-zero vector and $m$ is a non-zero scalar then $m\overrightarrow{a} $ is a unit vector if

asked May 8, 2013 by poojasapani_1

1 answer

If the equation $-2x+y+z=i\;;x-2y+z=m\;;x+y-2z=n$ such that $i+m+n=0,$ then the system has

asked May 8, 2013 by poojasapani_1

1 answer

If $f(x)=x^2$ $g(x)=sinx$, $\forall x\in R$, then the set of all $x$ satisfying $fogogof(x)=gogof(x)$ is

asked May 7, 2013 by rvidyagovindarajan_1

1 answer