If A=2i^-3j^+7k^, B=i^+2j^ and C=j^-k^. Find A·(B×C)

A·(B×C)=[ABC], volume of parallelepiped=2-3712001-1=2(-2-0)+3(-1-0)+7(1-0)=-4-3+7=0Therefore A, B and C are coplanar vectors.

A·(B×C)=[ABC], volume of parallelepiped=2-3712001-1=2(-2-0)+3(-1-0)+7(1-0)=-4-3+7=0Therefore A, B and C are coplanar vectors.

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If $A = 2 \hat{i} - 3 \hat{j} + 7 \hat{k}, B = \hat{i} + 2 \hat{j}$ and $C = \hat{j} - \hat{k}$ . Find $A \cdot (B \times C)$

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$A \cdot (B \times C) = [ABC]$ , volume of parallelepiped

$= |\begin{array}{r} 2 & - 3 & 7 \\ 1 & 2 & 0 \\ 0 & 1 & - 1 \end{array}| = 2 (- 2 - 0) + 3 (- 1 - 0) + 7 (1 - 0) = - 4 - 3 + 7 = 0$

Therefore A, B and C are coplanar vectors.

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