Question

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

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

Answer 1

The correct option is B ${60}^{\circ },{60}^{\circ },{45}^{\circ }$


Find the magnitude of given vector.
Given, vector$\overrightarrow{R}=\hat{i}+\hat{j}+\sqrt{2}\hat{k}$ Comparing the given vector 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 $|\overrightarrow{R}|=\sqrt{{R_x}^2+{R_y}^2+{R_z}^2}=2$
Find the angle made by the vector with $X,Y$ and $Z$ axes.
$\cos \alpha =\frac{R_x}{R}=\frac{1}{2}\Rightarrow \alpha ={60}^{\circ }$
$\cos \beta =\frac{R_y}{R}=\frac{1}{2}\Rightarrow \beta ={60}^{\circ }$
$\cos \gamma =\frac{R_z}{R}=\frac{1}{\sqrt{2}}\Rightarrow \beta ={45}^{\circ }$
Final Answer: (c)