Question

Solve this Question.

Evaluate the angle between vec a = I - 5j +7k and vec b = 8i + j + k​

Answer 1

Angle= 81.83°

Step-by-step explanation:

$\vec{a} = \hat{i} - 5 \hat{j} +7 \hat{k} \\ \vec{b} = 8 \hat{i} + \hat{ j }+ \hat {k} \\ \\\\ cos \theta = \frac{ \vec{a}. \vec{b}}{ |\vec{a}| |\vec{b}| } \\\\ = \frac{ (\hat{i} - 5 \hat{j} +7 \hat{k}).(8 \hat{i} + \hat{ j }+ \hat {k})}{ |\hat{i} - 5 \hat{j} +7 \hat{k}| |8 \hat{i} + \hat{ j }+ \hat {k}| } \\\\ = \frac{8 - 5 + 7}{ \sqrt{ {1}^{2} + ( - 5) ^{2} + {7}^{2} } \sqrt{ {8}^{2} + {1}^{2} + {1}^{2} } } \\\\ = \frac{10}{ \sqrt{1 + 25 + 49} \sqrt{64 + 1 + 1} } \\\\ = \frac{10}{ \sqrt{75} \sqrt{66} } \\\\ = \frac{10}{ \sqrt{4950} } \\\\ \\ = \frac{10}{15 \sqrt{22} } \\\\ = \frac{2}{3 \sqrt{22} } \\\\ \theta = {cos}^{ - 1} \frac{2}{3 \sqrt{22 } } \\ \\= 81.83 \degree$