Question

The angle between the two vectors $\overrightarrow{A} = 3\widehat{i} + 4\widehat{j} + 5\widehat{k}$ and $\overrightarrow{B} = 3\widehat{i} + 4\widehat{j} - 5\widehat{k}$ will be

• A. 90°
• B. 0°
• C. 60°
• D. 45°

Answer 1

Answer: (A)

90°

Answer 2

$\cos\theta = \frac{\overset{\rightarrow}{A}.\overset{\rightarrow}{B}}{|A||B|} = \frac{(3\widehat{i} + 4\widehat{j} + 5\widehat{k})(3\widehat{i} + 4\widehat{j} - 5\widehat{k})}{\sqrt{9 + 16 + 25}\sqrt{9 + 16 + 25}}$

$= \frac{9 + 16 - 25}{50} = 0$

⇒ $\cos\theta = 0$, $\therefore$ $\theta = 90{^\circ}$