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Question: If \(|\overset{\rightarrow}{A} \times \overset{\rightarrow}{B}| = |\overset{\rightarrow}{A}.\overset...

If ∣A→×B→∣=∣A→.B→∣,|\overset{\rightarrow}{A} \times \overset{\rightarrow}{B}| = |\overset{\rightarrow}{A}.\overset{\rightarrow}{B}|,then angle between A→\overset{\rightarrow}{A}and B→\overset{\rightarrow}{B} will be

A

30°

B

45°

C

60°

D

90°

Answer

45°

Explanation

Solution

∣A→×B→∣=A→.B→|\overrightarrow{A} \times \overrightarrow{B}| = \overrightarrow{A}.\overrightarrow{B}⇒ABsin⁡θ=ABcos⁡θAB\sin\theta = AB\cos\theta⇒tan⁡θ=1\tan\theta = 1

∴ θ=45∘\theta = 45{^\circ}