The direction cosines of a line which is perp | vedclass

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(D) Let the direction ratios of the two given lines be $\vec{b_1} = 2\hat{i} - 3\hat{j} + 1\hat{k}$ and $\vec{b_2} = 1\hat{i} + 2\hat{j} - 2\hat{k}$.S

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$\pm\frac{4}{3\sqrt{10}}, \pm\frac{5}{3\sqrt{10}}, \pm\frac{7}{3\sqrt{10}}$

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(D) Let the direction ratios of the two given lines be $\vec{b_1} = 2\hat{i} - 3\hat{j} + 1\hat{k}$ and $\vec{b_2} = 1\hat{i} + 2\hat{j} - 2\hat{k}$.Since the required line is perpendicular to both, its direction vector $\vec{v}$ is given by the cross product $\vec{b_1} 	imes \vec{b_2}$.$\vec{v} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 2 & -3 & 1 \ 1 & 2 & -2 \end{vmatrix} = \hat{i}(6 - 2) - \hat{j}(-4 - 1) + \hat{k}(4 + 3) = 4\hat{i} + 5\hat{j} + 7\hat{k}$.The magnitude of $\vec{v}$ is $|\vec{v}| = \sqrt{4^2 + 5^2 + 7^2} = \sqrt{16 + 25 + 49} = \sqrt{90} = 3\sqrt{10}$.The direction cosines are $\pm \frac{4}{3\sqrt{10}}, \pm \frac{5}{3\sqrt{10}}, \pm \frac{7}{3\sqrt{10}}$.

The direction cosines of a line which is perpendicular to the lines $\frac{x - 7}{2} = \frac{y + 17}{-3} = \frac{z - 6}{1}$ and $\frac{x + 5}{1} = \frac{y + 3}{2} = \frac{z - 6}{-2}$ are...

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