Question

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

• A. $\frac { x - 2 } { 4 } = \frac { y + 1 } { 1 } = \frac { z + 1 } { 1 }$
• B. $\frac { x + 2 } { 4 } = \frac { y - 1 } { 1 } = \frac { z - 1 } { 1 }$
• C. $\frac { x - 2 } { - 1 } = \frac { y + 1 } { 1 } = \frac { z + 1 } { 3 }$
• D. $\frac { x + 2 } { - 1 } = \frac { y - 1 } { 1 } = \frac { z - 1 } { 3 }$

Answer 1

Answer: (C)

$\frac { x - 2 } { - 1 } = \frac { y + 1 } { 1 } = \frac { z + 1 } { 3 }$

Answer 2

Let direction cosines of straight line be l, m, n

⇒ 4l + m + n = 0,

l – 2m + n = 0

⇒

⇒ .

Equation of straight line is $\frac { x - 2 } { - 1 } = \frac { y + 1 } { 1 } = \frac { z + 1 } { 3 }$