Motion in a Plane — Physics STD 11 Science — Question

2. 90°

Explanation:

Given $\vec{\text{A}}=\hat{\text{i}}+\hat{\text{j}}$

$\vec{\text{B}}=\hat{\text{i}}-\hat{\text{j}}$

$\vec{\text{A}}.\vec{\text{B}}=|\text{A}||\text{B}|\cos\theta$

$\cos\theta=\frac{\vec{\text{A}}.\vec{\text{B}}}{|\text{A}||\text{B}|}$

$=\frac{(\hat{\text{i}}+\hat{\text{j}}).(\hat{\text{i}}-\hat{\text{j}})}{\sqrt{1^2+1^2}\times\sqrt{1^2+(-1)^2}}=\frac{1-1}{2}=0$

$\Rightarrow\cos\theta=\cos90$

$\therefore\theta=90^\circ.$ Hence, verifies the option (b).