Question

Equation of line $BA$ is $x+y=1$. Find a unit vector along the reflected ray $AC$.

• A. $\frac{(\hat{i}+\hat{j})}{\sqrt{2}}$
• B. $\frac{(\hat{i}-\hat{j})}{\sqrt{2}}$
• C. $\sqrt{2}\left(\begin{array}{c}\hat{i}+\hat{j}\end{array}\right)$
• D. $\hat{i}+\hat{j}$

Answer 1

The correct option is A $\frac{(\hat{i}+\hat{j})}{\sqrt{2}}$

Here $\alpha ={45}^{\circ }$ so inclination of $AC$ with x-axis is ${45}^{\circ }$. So unit vector along $AC=cos{45}^{\circ }\hat{i}+sin{45}^{\circ }\hat{j}=\frac{\hat{i}+\hat{j}}{\sqrt{2}}$