Question

The angle between $\hat{i}$ and line of the intersection of the plane $\overrightarrow{r}\cdot (\hat{i}+2\hat{j}+3\hat{k})=0$ and $\overrightarrow{r}\cdot (3\hat{i}+3\hat{j}+\hat{k})=0$ is:

• A. ${\cos }^{-1}\left(\frac{1}{3}\right)$
• B. $co{s}^{-1}\left(\frac{1}{\sqrt{3}}\right)$
• C. ${\cos }^{-1}\left(\frac{2}{\sqrt{3}}\right)$
• D. None of these.

Answer 1

The correct option is D None of these.

D.r s of the line of the intersection of give planes are

$(i+2j+3k)\times (3i+3j+k)=-7i+8j-3k$
Now angle with $i$ is

$={\cos }^{-1}\left(\left|\frac{-7}{\sqrt{49+64+9}}\right|\right)$

$={\cos }^{-1}\frac{7}{\sqrt{122}}$