Question

the vector a and b are such that a+b=a-b, then the angle between a and bill be

Answer 1

Answer:

Let us suppose the angle (defined from a to b clockwise) between the vectors is θ,0≤θ≤2π. Then using the parallelogram rule for vector addition, and the law of cosines

|a+b|2 = |a|2 + |b|2 − 2|a||b|cosθ.

Similarly, recognizing that the angle between a and −b is π−θ, we get

|a−b|2 = |a|2 + |b|2 − 2|a||b|cos(π−θ) = |a|2 + |b|2 + 2|a||b|cosθ.

As, |a+b| = |a−b|,

|a|2 + |b|2 − 2|a||b|cosθ = |a|2 + |b|2 + 2|a||b|cosθ.

Or, on simplification, cosθ = 0.

Hence, θ = π/2 or 3π/2.