If two vectors 2hat{i} + 3hat{j} - hat{k} and | vedclass

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(B) Let $\vec{A} = 2\hat{i} + 3\hat{j} - \hat{k}$ and $\vec{B} = -4\hat{i} - 6\hat{j} + \lambda\hat{k}$.If two vectors $\vec{A} = a_1\hat{i} + a_2\hat

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$2$

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(B) Let $\vec{A} = 2\hat{i} + 3\hat{j} - \hat{k}$ and $\vec{B} = -4\hat{i} - 6\hat{j} + \lambda\hat{k}$.If two vectors $\vec{A} = a_1\hat{i} + a_2\hat{j} + a_3\hat{k}$ and $\vec{B} = b_1\hat{i} + b_2\hat{j} + b_3\hat{k}$ are parallel,then their components must be proportional:$\frac{a_1}{b_1} = \frac{a_2}{b_2} = \frac{a_3}{b_3}$.Substituting the given values:$\frac{2}{-4} = \frac{3}{-6} = \frac{-1}{\lambda}$.Simplifying the ratios:$-\frac{1}{2} = -\frac{1}{2} = -\frac{1}{\lambda}$.Equating the last two parts:$-\frac{1}{2} = -\frac{1}{\lambda} \implies \lambda = 2$.

If two vectors $2\hat{i} + 3\hat{j} - \hat{k}$ and $-4\hat{i} - 6\hat{j} + \lambda\hat{k}$ are parallel to each other,then the value of $\lambda$ is:

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