Question

Given that for two vectors a and b ,|axb|=|a.b|.find the acute angle between a and b

Answer 1

A/C to question,
|a × b| = |a.b|

We know, |a × b| = |a||b| sinθ [ where θ is the angle between a and b ]
also |a.b| = |a||b|cosθ , use these above

|a||b|sinθ = |a||b|cosθ
⇒sinθ = cosθ
⇒ sinθ/cosθ = 1
⇒ tanθ = 1 = tan45° ⇒θ = 45°

Hence, angle between a and b is 45°

Answer 2

Answer:

A/C to question,

|a × b| = |a.b|  

We know, |a × b| = |a||b| sinθ [ where θ is the angle between a and b ]

also |a.b| = |a||b|cosθ , use these above

|a||b|sinθ = |a||b|cosθ

⇒sinθ = cosθ

⇒ sinθ/cosθ = 1

⇒ tanθ = 1 = tan45° ⇒θ = 45°

Hence, angle between a and b is 45°

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