Question

If |a+ b|=|a- b| prove that the angle between a and b is 90°

Answer 1

Explanation:

|b|. cos t. Hence if a,b are nonzero, then after cancelling off same terms and dividing by |a| |b|, we get cos t =0, and so the angle t between them is 90°.

Answer 2

Given:

|a+ b|=|a- b|

To Find:

The proof of angle between a and b being 90°.

Solution:

We have been given that

|a+ b|=|a- b|

Now squaring both sides we get

  $|a+ b|^{2} = |a- b|^{2}$

⇒ $a^{2} + b^{2} + 2a.b = a^{2} + b^{2} - 2a.b$

⇒ $2a.b + 2a.b = 0$

⇒ $4a.b = 0$

⇒ $a.b = 0$

⇒ $|a||b|cos$ ∅ $= 0$

⇒ cos∅ = 0

⇒ ∅ = 90°

So between a and b is 90°.

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