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Question

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

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

A

(a×a).(b×b)(\mathbf{a} \times \mathbf{a}).(\mathbf{b} \times \mathbf{b})

B

(a.a)(b.b)(\mathbf{a}.\mathbf{a})(\mathbf{b}.\mathbf{b})

C

∣(a×b)∣(a.b)|(\mathbf{a} \times \mathbf{b})|(\mathbf{a}.\mathbf{b})

D

2(a.b)(a.b)2(\mathbf{a}.\mathbf{b})(\mathbf{a}.\mathbf{b})

Answer

(a.a)(b.b)(\mathbf{a}.\mathbf{a})(\mathbf{b}.\mathbf{b})

Explanation

Solution

We know (a×b)2+(a.b)2=a2b2=(a.a)(b.b)(\mathbf{a} \times \mathbf{b})^{2} + (\mathbf{a}.\mathbf{b})^{2} = a^{2}b^{2} = (\mathbf{a}.\mathbf{a})(\mathbf{b}.\mathbf{b}).