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Question: If \(\mathbf{a} = \mathbf{i} - \mathbf{j} + \mathbf{k},\mathbf{b} = \mathbf{i} + 2\mathbf{j} - \math...

If a=i−j+k,b=i+2j−k\mathbf{a} = \mathbf{i} - \mathbf{j} + \mathbf{k},\mathbf{b} = \mathbf{i} + 2\mathbf{j} - \mathbf{k} and c=3i+pj+5k\mathbf{c} = 3\mathbf{i} + p\mathbf{j} + 5\mathbf{k} are coplanar then the value of p will be

A

– 6

B

– 2

C

2

D

6

Answer

– 6

Explanation

Solution

1 & - 1 & 1 \\ 1 & 2 & - 1 \\ 3 & p & 5 \end{matrix} \right| = 0 \Rightarrow p = - 6.$$