Question

The angle between the planes, $\overrightarrow{r}.(2\hat{i}-\hat{j}+\hat{k})=6$ and $\overrightarrow{r}.(\hat{i}+\hat{j}+2\hat{k})=5$ , is:

• A. $\frac{\pi }{3}$
• B. $\frac{2\pi }{3}$
• C. $\frac{\pi }{6}$
• D. $\frac{5\pi }{6}$

Answer 1

The correct option is A $\frac{\pi }{3}$

Angle between $2x-y+z=6$ & $x+y+2z=5$ is
$\theta ={\cos }^{-1}\left[\frac{(2i-j+k).(i+j+2k)}{\sqrt{(2^2+1^2+1^2)(1^2+1^2+2^2)}}\right]=\frac{\pi }{3}$
Ans: B