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-

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

\dots

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