The direction ratios of the line perpendicula | vedclass

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Question

(A) Let $\vec{a}$ and $\vec{b}$ be the vectors along the lines whose direction ratios are $2, 3, 1$ and $1, 2, 1$ respectively. $\vec{a} = 2\hat{i} +

Vedclass · Accepted Answer

$1, -1, 1$

Vedclass · Answer

(A) Let $\vec{a}$ and $\vec{b}$ be the vectors along the lines whose direction ratios are $2, 3, 1$ and $1, 2, 1$ respectively. $\vec{a} = 2\hat{i} + 3\hat{j} + \hat{k}$ and $\vec{b} = \hat{i} + 2\hat{j} + \hat{k}$. $A$ vector perpendicular to both $\vec{a}$ and $\vec{b}$ is given by their cross product $\vec{a} 	imes \vec{b}$. $\vec{a} 	imes \vec{b} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 2 & 3 & 1 \ 1 & 2 & 1 \end{vmatrix} = \hat{i}(3-2) - \hat{j}(2-1) + \hat{k}(4-3) = \hat{i} - \hat{j} + \hat{k}$. Thus,the direction ratios are $1, -1, 1$. Comparing this with the given options,the correct choice is $A$.

The direction ratios of the line perpendicular to the lines having direction ratios $2, 3, 1$ and $1, 2, 1$ are

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