MATCH THE FOLLOWING:
(A) The D.R. of the line which is perpendicular to lines $\frac{x-7}{2} = \frac{y+17}{-3} = \frac{z-6}{-1}$ and $\frac{x+5}{-1} = \frac{y+3}{2} = \frac{z-4}{-2}$ is
Step-by-Step Solution
Key Concept: The direction vector perpendicular to two lines is found using the cross product of their respective direction vectors.
To find the direction ratios (D.R.) of a line perpendicular to two given lines, we use the cross product of their direction vectors. The first line has D.R. $\vec{d_1} = (2, -3, -1)$ and the second has D.R. $\vec{d_2} = (-1, 2, -2)$. The perpendicular direction is $\vec{d_1} \times \vec{d_2} = \begin{vmatrix} \vec{i} & \vec{j} & \vec{k} \\ 2 & -3 & -1 \\ -1 & 2 & -2 \end{vmatrix} = \vec{i}(6+2) - \vec{j}(-4-1) + \vec{k}(4-3) = (8, 5, 1)$. Thus the D.R. is $(8, 5, 1)$ or any scalar multiple like $(8k, 5k, k)$.
Correct Answer: (8, 5, 1)