Solveeit Logo
Login

Question

Question: If **a**, **b**, **c** are three non-coplanar vector, then \(\frac{\mathbf{a}.\mathbf{b} \times \mat...

If a, b, c are three non-coplanar vector, then a.b×cc×a.b+b.a×cc.a×b\frac{\mathbf{a}.\mathbf{b} \times \mathbf{c}}{\mathbf{c} \times \mathbf{a}.\mathbf{b}} + \frac{\mathbf{b}.\mathbf{a} \times \mathbf{c}}{\mathbf{c}.\mathbf{a} \times \mathbf{b}}=

A

0

B

2

C

– 2

D

None of these

Answer

0

Explanation

Solution

a.b×cc×a.b+b.a×cc.a×b=[abc][cab]+[bac][cab]=[abc][cab]−[abc][cab]=0.\frac{\mathbf{a}.\mathbf{b} \times \mathbf{c}}{\mathbf{c} \times \mathbf{a}.\mathbf{b}} + \frac{\mathbf{b}.\mathbf{a} \times \mathbf{c}}{\mathbf{c}.\mathbf{a} \times \mathbf{b}} = \frac{\lbrack\mathbf{abc}\rbrack}{\lbrack\mathbf{cab}\rbrack} + \frac{\lbrack\mathbf{bac}\rbrack}{\lbrack\mathbf{cab}\rbrack} = \frac{\lbrack\mathbf{abc}\rbrack}{\lbrack\mathbf{cab}\rbrack} - \frac{\lbrack\mathbf{abc}\rbrack}{\lbrack\mathbf{cab}\rbrack} = 0.