Question

What is the angle between vector $\overrightarrow{A}=\hat{i}+\hat{j}+\sqrt{2}\hat{k}$ and the Z-axis :

• A. $0^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is B ${45}^{\circ }$

Z-axis can be represented as $\hat{k}$
Thus angle is $cos\theta =\frac{\overrightarrow{A}.\hat{k}}{|\overrightarrow{A}|.|\hat{k}|}=\frac{(\hat{i}+\hat{j}+\sqrt{2}\hat{k}).\hat{k}}{\sqrt{1+1+2}.1}=\frac{\sqrt{2}}{2}$
Thus, $cos\theta =1/\sqrt{2}$ or $\theta ={45}^0$