Question

If two vector $\vec{A} = 2 \hat{i} + 3 \hat{j} - \hat{k} and - 4 \hat{i} - 6 \hat{j} - λ \hat{k}$ are parallel to each other then value of $λ$

Moderate

Solution

Let $\vec{A} = 2 \hat{i} + 3 \hat{j} - \hat{k} and - 4 \hat{i} - 6 \hat{j} + λ \hat{k}$
$\vec{A} and \vec{B}$ are parallel to each other
$\frac{a_{1}}{b_{1}} = \frac{a_{2}}{b_{2}} = \frac{a_{3}}{b_{3}} i . e ., \frac{2}{- 4} = \frac{3}{- 6} = \frac{- 1}{λ} \Rightarrow λ = 2$

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