The direction cosines of a line which is perp | vedclass

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(B) Let $\vec{a} = 3\hat{i} - 2\hat{j} + 4\hat{k}$ and $\vec{b} = 1\hat{i} + 3\hat{j} - 2\hat{k}$.Since the line is perpendicular to both lines,its di

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$\frac{-8}{\sqrt{285}}, \frac{10}{\sqrt{285}}, \frac{11}{\sqrt{285}}$

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(B) Let $\vec{a} = 3\hat{i} - 2\hat{j} + 4\hat{k}$ and $\vec{b} = 1\hat{i} + 3\hat{j} - 2\hat{k}$.Since the line is perpendicular to both lines,its direction vector is given by the cross product $\vec{n} = \vec{a} 	imes \vec{b}$.$\vec{n} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 3 & -2 & 4 \ 1 & 3 & -2 \end{vmatrix} = \hat{i}(4 - 12) - \hat{j}(-6 - 4) + \hat{k}(9 + 2) = -8\hat{i} + 10\hat{j} + 11\hat{k}$.The magnitude of the vector is $|\vec{n}| = \sqrt{(-8)^2 + 10^2 + 11^2} = \sqrt{64 + 100 + 121} = \sqrt{285}$.The direction cosines are the components of the unit vector,which are $\frac{-8}{\sqrt{285}}, \frac{10}{\sqrt{285}}, \frac{11}{\sqrt{285}}$.

The direction cosines of a line which is perpendicular to lines whose direction ratios are $3, -2, 4$ and $1, 3, -2$ are

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