Question

The direction ratio of the line which is perpendicular to the lines $\frac { x - 7 } { 2 } = \frac { y + 17 } { - 3 } = \frac { z - 6 } { 1 }$ and $\frac { x + 5 } { 1 } = \frac { y + 3 } { 2 } = \frac { z - 4 } { - 2 }$ are

• A. < 4, 5, 7 >
• B. < 4, –5, 7 >
• C. < 4, –5, –7 >
• D. < –4, 5, 7 >

Answer 1

Answer: (A)

< 4, 5, 7 >

Answer 2

Let d.r.’s of line be l, m, n.

∵ line is perpendicular to given line

∴ $2 l - 3 m + n = 0$ ……(i)

$l + 2 m - 2 n = 0$ ……(ii)

From equation (i) and (ii)

$\frac { l } { 6 - 2 } = \frac { m } { 1 + 4 } = \frac { n } { 4 + 3 }$ or $\frac { l } { 4 } = \frac { m } { 5 } = \frac { n } { 7 }$.

Hence, d.r.’s of line (< 4, 5, 7 >)