Question

The angle between planes $\overline{r}.(2\overline{i}-3\overline{j}+4\overline{k})+11=0$ and $\overline{r}.(3\overline{i}-2\overline{j}-3\overline{k})+27=0$ is

• A. $\frac{\pi }{6}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{3}$
• D. $\frac{\pi }{2}$

Answer 1

The correct option is D $\frac{\pi }{2}$

$cos\theta =\frac{a_1{a}_2+b_1{b}_2+c_1{c}_2}{\sqrt{a_1^2+b_1^2+c_1^2}\sqrt{a_2^2+b_2^2+c_2^2}}$

$\Rightarrow cos\theta =\frac{6+6-12}{\sqrt{4+9+16}\sqrt{9+4+9}}$

$\therefore cos\theta =0$

$\therefore \theta =\frac{\pi }{2}$