Question
The angle between $\vec{\text{A}}=\hat{\text{i}}+\hat{\text{j}}$ and $\vec{\text{B}}=\hat{\text{i}}-\hat{\text{j}}$ is
- 45°
- 90°
- –45°
- 180°
✓
Answer
- 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).
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