Question

Write the direction cosines of the vector \[\hat{i} + 2 \hat{j} + 3 \hat{k}\].

Answer 1

Given: \[\hat{i} + 2 \hat{j} + 3 \hat{k}\]
Then, direction cosines are \[\frac{1}{\sqrt{1^2 + 2^2 + 3^2}}, \frac{2}{\sqrt{1^2 + 2^2 + 3^2}} , \frac{3}{\sqrt{1^2 + 2^2 + 3^2}}\] or, \[\frac{1}{\sqrt{14}}, \frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}}\].