Question

What is the cosine of the angle which the vector $\sqrt{2}\hat{i}+\hat{j}+\hat{k}$ makes with y-axis?

Answer 1

Given $\sqrt{2}\hat{i}+\hat{j}+\hat{k}$ .
Therefore , direction cosines are $\frac{\sqrt{2}}{\sqrt{{\left(\sqrt{2}\right)}^2+1^2+1^2}},\frac{1}{\sqrt{{\left(\sqrt{2}\right)}^2+1^2+1^2}},\frac{1}{\sqrt{{\left(\sqrt{2}\right)}^2+1^2+1^2}}$ or $\frac{1}{\sqrt{2}},\frac{1}{2},\frac{1}{2}$

So, cosine angle with respect to y-axis is $\frac{1}{2}$