The direction ratios of the line perpendicular to the lines $\frac{x-7}{-6}=\frac{y+17}{4}=\frac{z-6}{2}$ and $\frac{x+5}{6}=\frac{y+3}{3}=\frac{z-4}{-6}$ are proportional to :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 5, 4, 7
$\vec{v_1}||l_1=-6\hat i+4\hat j+2\hat k$
$\vec{v_2}||l_2=6\hat i+3\hat j-6\hat k$
$\vec{P_1}||\vec{v_1}=-3\hat i+2\hat j+\hat k$
$\vec{P_2}||\vec{v_2}=2\hat i+\hat j-2\hat k$
$\vec{P_1}×\vec{P_2}=\begin{vmatrix}\hat i&\hat j&\hat k\\-3&2&1\\2&1&-2\end{vmatrix}$
$=-5\hat i-4\hat j-7\hat k$
$\vec{P_2}×\vec{P_1}=5\hat i+4\hat j+7\hat k$
DR → 5, 4, 7