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Question Number 141129 by bobhans last updated on 16/May/21

F o r w h a t v a l u e s o f λ a r e t h e

v e c t o r s λ \hat{i} + 2 \hat{j} + \hat{k}, 3 \hat{i} + 4 \hat{j} + λ \hat{k}

, \hat{j} + \hat{k} c o p l a n a r

Answered by EDWIN88 last updated on 16/May/21

(\begin{matrix} 3 \\ 4 \\ λ \end{matrix}) = m (\begin{matrix} λ \\ 2 \\ 1 \end{matrix}) + n (\begin{matrix} 0 \\ 1 \\ 1 \end{matrix})

\Rightarrow m λ = 3; λ = \frac{3}{m}

\Rightarrow {\begin{cases} 2 m + n = 4 \\ m + n = λ \end{cases} \Rightarrow m = 4 - λ

\Rightarrow m = 4 - \frac{3}{m}; m^{2} - 4 m + 3 = 0

\Rightarrow (m - 1) (m - 3) = 0 {\begin{cases} m = 1 \Rightarrow λ = 3 \\ m = 3 \Rightarrow λ = 1 \end{cases}

λ = {1, 3} ⋇

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