Question

If direction ratios of the normal of the plane which contains the lines $\frac{x-2}{3}=\frac{y-4}{2}=\frac{z-1}{1}$ and $\frac{x-6}{3}=$ $\frac{y+2}{2}=\frac{z-2}{1}$ are $(a, 1,-26)$, then $a$ is equal to

Answer 1

The given lines are parallel

$\vec{n} =\overrightarrow{A B} \times(3 \hat{i}+2 \hat{j}+\hat{k})$
$=(4 \hat{i}-6 \hat{j}+\hat{k}) \times(3 \hat{i}+2 \hat{j}+\hat{k})$
$=-8 \hat{i}-\hat{j}+26 \hat{k}$
$\Rightarrow$ Direction ratios of normal are $(8,+1,-26)$
$\Rightarrow a=8$