Question

A and b are two unit vectors such that a + b is also a unit vector find angle between them

Answer 1

Answer:

120°

Step-by-step explanation:

Let θ be the angle between a and b, with 0° ≤ θ ≤ 180°.

|a+b| = 1

=> ( a + b ) · ( a + b ) = 1

=> a·a + b·b + 2a·b = 1

=> |a|² + |b|² + 2a·b = 1

=> 1 + 1 + 2a·b = 1                [ since a and b are unit vectors ]

=> 2a·b = -1

=> a·b = -1/2

=> |a| |b| cos θ = -1/2

=> cos θ = -1/2               [ since a and b are unit vectors ]

=> θ = 120°

Answer 2

|a|=1 |b|=1 |a+b|=1

so, |a+b|=√{|a|² + |b|² +2|a||b|cos∆}

where ∆= angle between two vectors

take a square at both side

|a+b|² = |a|² + |b|² +2|a||b|cos∆

now put the value

1=1+1+2(cos∆)

-1=2(cos∆)

cos∆=-1/2

∆=π-π/3

∆=2π/3

∆=120°

thanks