Question

The angle between the vectors $\overline{a}=\overline{i}+2\overline{j}+2\overline{k};\overline{b}=2\overline{i}+2\overline{j}+\overline{k}$ is

• A. ${\cos }^{-1}\left(8/9\right)$
• B. ${\cos }^{-1}\left(9/8\right)$
• C. ${\cos }^{-1}\left(3/2\right)$
• D. ${\cos }^{-1}\left(2/3\right)$

Answer 1

The correct option is A ${\cos }^{-1}\left(8/9\right)$

$\overrightarrow{a}\cdot \overrightarrow{b}=|\overrightarrow{a}||\overrightarrow{b}|\cos \theta$

$\left(1\right)\left(2\right)+\left(2\right)\left(2\right)+\left(2\right)\left(1\right)=\sqrt{1^2+2^2+2^2\sqrt{2^2+2^2+1^2}}\cos \theta$

$8=3\times 3\cos \theta$

$\cos \theta =\frac{8}{9}$

$\theta ={\cos }^{-1}\left(\frac{8}{9}\right)$