# If A.B = |A × B| and A, B are vectors then find angle between vectors A and B

It’s given that A.B = |A × B|
Here A, B are vectors

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

A.B = |A × B| (Equation 1)

Using formulas for Dot and Cross products
A.B = |A| |B| Cosθ

|A × B| = |A| |B| Sinθ

Therefore (Equation 1) can be written as
|A| |B| Cosθ = |A| |B| Sinθ

Cosθ = Sinθ

1 = Sinθ/Cosθ = Tanθ

Tanθ = 1

General Solution for Tanθ = 1 is θ = (4n + 1)𝛑/4 where is n is some integer

Therefore if A.B = |A × B| and A, B are vectors then possible values of angles between vectors A and B are 𝛑/4, 5𝛑/4, 9𝛑/4 and so on.

👇🏻 Key Concepts Used in This Question

1. 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

2. Cross Product of two vectors a and b is defined as a × b = |a| |b| Sinθ n
Where
a, b are two vectors
|a|, |b| are magnitudes of these vectors
θ is the angle between directions of vectors a, b
n is a unit vector pointing in direction of a × b vector
(Cross Product is also known as Vector Product)

3. General Solution for Tanθ = 1 is θ = (4n + 1)𝛑/4 where is n is some integer