If a^→ =(4,2,−1), b^→ =(m,1,1) c^→ =(3^� −1,0) are three vectors then find the value of m such that a^→ ,b^→ and c^→ are coplanar and find a^→ ×(b^→ ×c^→ ).


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Question Number 135423 by benjo_mathlover last updated on 13/Mar/21

$I f \vec{a} = (4, 2, - 1), \vec{b} = (m, 1, 1)$ $\vec{c} = (\bar{3} - 1, 0) a r e t h r e e v e c t o r s$ $t h e n f i n d t h e v a l u e o f m s u c h$ $t h a t \vec{a}, \vec{b} a n d \vec{c} a r e c o p l a n a r a n d$ $f i n d \vec{a} \times (\vec{b} \times \vec{c}) .$
	Answered by mr W last updated on 13/Mar/21

	$a \times c = \| \begin{matrix} 4 & 2 & - 1 \\ 3 & - 1 & 0 \end{matrix} \| = (- 1, - 3, - 10)$ $(a \times c) \cdot b = - 1 \times m - 3 \times 1 - 10 \times 1 = 0$ $\Rightarrow m = - 13$ $. . .$
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