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Question: If \(|\mathbf{a}| = 3,|\mathbf{b}| = 4\) and \(|\mathbf{a} + \mathbf{b}| = 5,\) then \(|\mathbf{a} -...

If ∣a∣=3,∣b∣=4|\mathbf{a}| = 3,|\mathbf{b}| = 4 and ∣a+b∣=5,|\mathbf{a} + \mathbf{b}| = 5, then ∣a−b∣=|\mathbf{a} - \mathbf{b}| =

A

6

B

5

C

4

D

3

Answer

5

Explanation

Solution

We have ∣a+b∣2+∣a−b∣2=2(∣a∣2+∣b∣2)|\mathbf{a} + \mathbf{b}|^{2} + |\mathbf{a} - \mathbf{b}|^{2} = 2(|\mathbf{a}|^{2} + |\mathbf{b}|^{2})

∴25+∣a−b∣2=2(9+16)⇒∣a−b∣=5\therefore 25 + |\mathbf{a} - \mathbf{b}|^{2} = 2(9 + 16) \Rightarrow |\mathbf{a} - \mathbf{b}| = 5.