If |A + B| = A.B what is angle between A & B

In this question, we are given two vectors A and B
It’s also given that |A + B| = A.B

Here
|A + B| = Magnitude of vector (A + B)
A.B = Dot Product of vectors A and B

We need to figure out what’s angle between vectors A and B

Best way to figure this out is to start with given equation |A + B| = A.B

Simplifying right hand side of equation |A + B| = A.B
using Dot Product formula

|A + B| = |A| |B| Cosθ

Where θ is angle between vectors A and B

⇒ Cosθ = |A + B|/|A| |B|

θ = Cos-1{|A + B|/|A| |B|}

Therefore if |A + B| = A.B and A, B are vectors then angle between vectors A, B is Cos-1{|A + B|/|A| |B|}

👇🏻 Key Concepts Used in This Question

Dot Product of two vectors a and b is defined as a.b = |a| |b| Cosθ
Where
a, b are two vectors
|a|, |b| are magnitudes of these vectors
θ is the angle between directions of vectors a, b


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