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Question: If **a, b, c** be any three non-coplanar vectors, then \(\left[ \begin{array} { l l l } \mathbf { ...

If a, b, c be any three non-coplanar vectors,

then [a+bb+cc+a]=\left[ \begin{array} { l l l } \mathbf { a } + \mathbf { b } & \mathbf { b } + \mathbf { c } & \mathbf { c } + \mathbf { a } \end{array} \right] =

A
B

2

C

[abc]2[ \mathbf { a } \mathbf { b } \mathbf { c } ] ^ { 2 }

D
Answer

2

Explanation

Solution

=(a+b).(b×c+b×a+c×c+c×a)= ( \mathbf { a } + \mathbf { b } ) . ( \mathbf { b } \times \mathbf { c } + \mathbf { b } \times \mathbf { a } + \mathbf { c } \times \mathbf { c } + \mathbf { c } \times \mathbf { a } )

, {∵c×c=0}\{ \because \mathbf { c } \times \mathbf { c } = 0 \}

+b.b×a+b.c×a+ \mathbf { b } . \mathbf { b } \times \mathbf { a } + \mathbf { b } . \mathbf { c } \times \mathbf { a }

.