Question

The angle between the planes $r.(2\hat{i}-\hat{j}+2\hat{k})=3$ and $r.(3\hat{i}-6\hat{j}+2\hat{k})=4$

• A. $Co{s}^{-1}\left(\frac{16}{21}\right)$
• B. $Si{n}^{-1}\left(\frac{4}{21}\right)$
• C. $Co{s}^{-1}\left(\frac{1}{4}\right)$
• D. $Co{s}^{-1}\left(\frac{3}{4}\right)$

Answer 1

The correct option is A $Co{s}^{-1}\left(\frac{16}{21}\right)$

Let $a=2\hat{i}-\hat{j}=2\hat{k},b=3\hat{i}-6\hat{j}+2\hat{k}$
If $\theta$ is the angle between the planes then
$cos\theta =cos(a,b)=\frac{ab}{|a||b|}=\frac{6+6+4}{\sqrt{4+1+4}\sqrt{9+36+4}}=\frac{16}{3\times 7}=\frac{16}{21}$