# What is the angle between <3 , -2 , 7 >  and  < 1, -3 , 6 > ?

May 13, 2016

$\implies \theta = {23.4}^{\circ}$

#### Explanation:

• Let First vector be $\vec{A} = 3 \hat{i} - 2 \hat{j} + 7 \hat{k}$
• $| \vec{A} | = \sqrt{{3}^{2} + {2}^{2} + {7}^{2}} = \sqrt{62}$
• and the 2nd vector be $\vec{B} = 1 \hat{i} - 3 \hat{j} + 6 \hat{k}$
• $| \vec{B} | = \sqrt{{1}^{2} + {3}^{2} + {6}^{2}} = \sqrt{46}$
• If the angle between them be $\theta$
then $\cos \theta = \frac{\vec{A} \cdot \vec{B}}{| \vec{A} | | \vec{B} |}$

$\implies \cos \theta = \frac{\left(3 \hat{i} - 2 \hat{j} + 7 \hat{k}\right) \cdot \left(1 \hat{i} - 3 \hat{j} + 6 \hat{k}\right)}{\sqrt{62} \cdot \sqrt{46}}$

$\implies \cos \theta = \frac{1 + 6 + 42}{\sqrt{62} \cdot \sqrt{46}} \approx 0.92$

$\implies \theta = {23.4}^{\circ}$