The angle between \(\vec{a}=3\hat{i}+\hat{j}+2\hat{k}, \vec{b}=2\hat{i}-2\hat{j}+4\hat{k}\) is
Answer & explanation
Correct answer: option 1
\(\vec{a}=3\hat{i}+\hat{j}+2\hat{k},\vec{b}=2\hat{i}-2\hat{j}+4\hat{k}\hspace{5cm}\)
\(\vec{a}\cdot \vec{b}=6-2+8=12,|\vec{a}|=\sqrt{14},|\vec{b}|=\sqrt{24}\hspace{5cm}\)
\(\begin{aligned}\cos \theta&=\frac{\vec{a}\cdot \vec{b}}{|\vec{a}||\vec{b}|}\\ &=\frac{12}{\sqrt{2\times 7\times 2^{3}\times 3}}\\ &=\frac{12}{4\sqrt{21}}\\ &=\frac{3}{\sqrt{21}}\\ &=\sqrt{\frac{3}{7}}\\ \theta&=\cos^{-1}\left(\sqrt{\frac{3}{7}}\right)\end{aligned}\)