Question

(a) Find the direction cosines of the vector \( \hat{i} + \hat{j} - 2\hat{k} \).

Hint:

Direction cosines are calculated by dividing each component by the magnitude of the vector.

Answer 1

Step1:Thedirectioncosinesarecalculatedas: \[ l=\frac{1}{\sqrt{1^2+1^2+(-2)^2}},\,m=\frac{1}{\sqrt{1^2+1^2+(-2)^2}},\,n=\frac{-2}{\sqrt{1^2+1^2+(-2)^2}}. \] Simplify: \[ l=m=\frac{1}{\sqrt{6}},\,n=\frac{-2}{\sqrt{6}}. \]