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Question: If **a** and **b** are mutually perpendicular vectors, then \((\mathbf{a} + \mathbf{b})^{2} =\)...

If a and b are mutually perpendicular vectors, then (a+b)2=(\mathbf{a} + \mathbf{b})^{2} =

A

a+b\mathbf{a} + \mathbf{b}

B

a−b\mathbf{a} - \mathbf{b}

C

a2−b2a^{2} - b^{2}

D

(a−b)2(\mathbf{a} - \mathbf{b})^{2}

Answer

(a−b)2(\mathbf{a} - \mathbf{b})^{2}

Explanation

Solution

It is obvious, since a.b=0.\mathbf{a}.\mathbf{b} = 0.

Hence (a+b)2=a2+b2=(a−b)2.(\mathbf{a} + \mathbf{b})^{2} = a^{2} + b^{2} = (\mathbf{a} - \mathbf{b})^{2}.