If the direction ratios of the lines L_1 and | vedclass

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(B) Let the direction ratios of the line perpendicular to both $L_1$ and $L_2$ be $(a, b, c)$. Since the line is perpendicular to both,its direction r

Vedclass · Accepted Answer

$\pm \frac{1}{\sqrt{35}}, \pm \frac{5}{\sqrt{35}}, \pm \frac{3}{\sqrt{35}}$

Vedclass · Answer

(B) Let the direction ratios of the line perpendicular to both $L_1$ and $L_2$ be $(a, b, c)$. Since the line is perpendicular to both,its direction ratios are given by the cross product of the direction ratios of $L_1$ and $L_2$: $(a, b, c) = (2, -1, 1) 	imes (3, -3, 4) = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 2 & -1 & 1 \ 3 & -3 & 4 \end{vmatrix} = \hat{i}(-4 + 3) - \hat{j}(8 - 3) + \hat{k}(-6 + 3) = -1\hat{i} - 5\hat{j} - 3\hat{k}$. Thus,the direction ratios are $(-1, -5, -3)$ or $(1, 5, 3)$. The magnitude is $\sqrt{1^2 + 5^2 + 3^2} = \sqrt{1 + 25 + 9} = \sqrt{35}$. The direction cosines are $\pm \frac{1}{\sqrt{35}}, \pm \frac{5}{\sqrt{35}}, \pm \frac{3}{\sqrt{35}}$.

If the direction ratios of the lines $L_1$ and $L_2$ are $2, -1, 1$ and $3, -3, 4$ respectively,then the direction cosines of a line that is perpendicular to both $L_1$ and $L_2$ are

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