Question

The angles which is a vector $\hat{i}+\hat{j}+\sqrt{2}\hat{k}$ makes with $X,y$ and $Z$ axes respectively are

• A. ${60}^o,{60}^o,{60}^o$
• B. ${45}^o,{45}^o,{45}^o$
• C. ${60}^o,{60}^o,{45}^o$
• D. ${45}^o,{45}^o,{60}^o$

Answer 1

The correct option is C ${60}^o,{60}^o,{45}^o$

$\overrightarrow{R}=\hat{i}+\hat{j}+\sqrt{2}\hat{k}$
Comparing the given vectro with $R=R_x\hat{i}+R_y\hat{j}+R_z\hat{k}$
$R_x=1,R_y=1,R_z=\sqrt{2}$ and $|\overrightarrow{R}|=\sqrt{R_x^2+R_y^2+R_z^2}=2$
$\cos \alpha =\frac{R_x}{R}=\frac{1}{2}\Rightarrow \alpha ={60}^o$
$\cos \beta =\frac{R_y}{R}=\frac{1}{2}\Rightarrow \beta ={60}^o$
$\cos \gamma =\frac{R_z}{R}=\frac{1}{\sqrt{2}}\Rightarrow \gamma ={45}^o$