A straight line passes through the point (2, –1, –1). It is parallel to the plane 4x + y + z + 2 = 0 and is perpendicular to the line $\frac{x}{1}=\frac{y}{-2}=\frac{z-5}{1}$. The equations of the straight line are
Answer & explanation
Correct answer: option 3
Let direction cosines of straight line be l, m, n
∴ 4l + m + n = 0
l – 2m + n = 0
$\Rightarrow \frac{I}{3}=\frac{m}{-3}=\frac{n}{-9} \Rightarrow \frac{I}{-1}=\frac{m}{+1}=\frac{n}{3}$
∴ Equation of straight line is $\frac{x-2}{-1}=\frac{y+1}{1}=\frac{z+1}{3}$
Hence (3) is the correct choice.