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Question: The angle between the vectors \((\widehat{i} + \widehat{j})\) and \((\widehat{j} + \widehat{k})\) is...

The angle between the vectors (i^+j^)(\widehat{i} + \widehat{j}) and (j^+k^)(\widehat{j} + \widehat{k}) is

A

30°

B

45°

C

60°

D

90°

Answer

60°

Explanation

Solution

(i^+j^).(j^+k^)=0+0+1+0=1(\widehat{i} + \widehat{j}).(\widehat{j} + \widehat{k}) = 0 + 0 + 1 + 0 = 1

cos⁡θ=A→.B→∣A→∣∣B→∣=12×2=12\cos\theta = \frac{\overrightarrow{A}.\overrightarrow{B}}{|\overrightarrow{A}||\overrightarrow{B}|} = \frac{1}{\sqrt{2} \times \sqrt{2}} = \frac{1}{2}∴ θ=60∘\theta = 60{^\circ}