If the direction ratios of two lines L_1 and | vedclass

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(A) Let the direction ratios of the line $L_1$ be $\vec{a} = (1, -2, 2)$ and the direction ratios of the line $L_2$ be $\vec{b} = (-2, 3, -6)$.To find

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$(6, 2, -1)$

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(A) Let the direction ratios of the line $L_1$ be $\vec{a} = (1, -2, 2)$ and the direction ratios of the line $L_2$ be $\vec{b} = (-2, 3, -6)$.To find the direction ratios of a line perpendicular to both $L_1$ and $L_2$,we calculate the cross product $\vec{n} = \vec{a} 	imes \vec{b}$.$\vec{n} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 1 & -2 & 2 \ -2 & 3 & -6 \end{vmatrix}$$= \hat{i}((-2)(-6) - (2)(3)) - \hat{j}((1)(-6) - (2)(-2)) + \hat{k}((1)(3) - (-2)(-2))$$= \hat{i}(12 - 6) - \hat{j}(-6 + 4) + \hat{k}(3 - 4)$$= \hat{i}(6) - \hat{j}(-2) + \hat{k}(-1)$$= (6, 2, -1)$.Thus,the direction ratios of the line perpendicular to both $L_1$ and $L_2$ are $(6, 2, -1)$.

If the direction ratios of two lines $L_1$ and $L_2$ are given by $(1, -2, 2)$ and $(-2, 3, -6)$ respectively,then the direction ratios of the line which is perpendicular to the lines $L_1$ and $L_2$ are

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