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Question: If \((\mathbf{a} \times \mathbf{b})^{2} + (\mathbf{a}.\mathbf{b})^{2} = 144\) and \(|\mathbf{a}| = 4...

If (a×b)2+(a.b)2=144(\mathbf{a} \times \mathbf{b})^{2} + (\mathbf{a}.\mathbf{b})^{2} = 144 and ∣a∣=4,|\mathbf{a}| = 4, then ∣b∣=|\mathbf{b}| =

A

16

B

8

C

3

D

12

Answer

3

Explanation

Solution

We know that (a×b)2+(a.b)2=∣a∣2∣b∣2(\mathbf{a} \times \mathbf{b})^{2} + (\mathbf{a}.\mathbf{b})^{2} = |\mathbf{a}|^{2}|\mathbf{b}|^{2}

∴144=16∣b∣2⇒∣b∣=3.\therefore 144 = 16|\mathbf{b}|^{2} \Rightarrow |\mathbf{b}| = 3.