Question

Give an example of vectors vector a and vector b such that vector |a| = vector |b| but vector a ≠ b.

Answer 1

Answer:

Step-by-step explanation:

If a and b are two vectors such that |a+b|=|a-b|, what is the angle between a and b?

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=π2 or 3π2.

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