Angle between two planes r (2 i-j+k)=6 and r (i+j+2 k)=5 is - Vidyadip

MCQ

Angle between two planes $\bar{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=6$ and $\bar{r} \cdot(\hat{i}+\hat{j}+2 \hat{k})=5$ is

A
$\frac{\pi}{6}$
B
$\frac{\pi}{4}$
✓
$\frac{\pi}{3}$
D
$\frac{\pi}{2}$

✓

Answer

Correct option: C.

$\frac{\pi}{3}$

(C)
$\bar{n}_1=2 \hat{i}-\hat{j}+\hat{k}$ and $\bar{n}_2=\hat{i}+\hat{j}+2 \hat{k}$
$\therefore \quad \cos \theta=\left|\frac{\bar{n}_1 \cdot \bar{n}_2}{\left|\overline{n_1}\right|\left|\overline{n_2}\right|}\right|$
$=\left|\frac{2(1)-1(1)+1(2)}{\sqrt{4+1+1} \sqrt{1+1+4}}\right|=\frac{1}{2}$
$\Rightarrow \theta=\frac{\pi}{3}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from Line and Plane→Line and Plane — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

The point at which the maximum value of $x + y,$ subject to the constraints $x + 2y ≤ 70, 2x + y ≤ 95, x, y ≥ 0$ isobtained, is:

The inverse of the matrix $A=\left[\begin{array}{ccc}2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3\end{array}\right]$ is

$\int_{-1}^1 x|x| d x=$

If m and n are the order and degree of the differential equation $(\text{y}_{2})^{5}+\frac{4(\text{y}_{2})^{3}}{\text{y}^{3}}+\text{y}^{3}=\text{y}_{3}=\text{x}^{2}-1$, then

$4 \tan ^{-1} \frac{1}{5}-\tan ^{-1} \frac{1}{70}+\tan ^{-1} \frac{1}{99}=$

Auxiliary equation of $2 x^2+3 x y-9 y^2=0$ is________

Let $f(x)=5-|x-2|$ and $g(x)=|x+1|, x \in R$ If $f(x)$ attains maximum value at $\alpha$ and $g(x)$ attains minimum value at $\beta$, then $\lim _{x \rightarrow-\alpha \beta} \frac{(x-1)\left(x^2-5 x+6\right)}{x^2-6 x+8}$ is equal to

If $|\bar{a}|=3,|\bar{b}|=4$ and the angle between $\bar{a}$ and $\overline{ b }$ is $120^{\circ}$, then $|4 \overline{ a }+3 \overline{b}|$ is equal to

If a matrix $A$ is such that $4 A^3+2 A^2+7 A+I=0$, then $A^{-1}$ equals

The value of $\cos ^{-1}(-1)$ is