Question

The direction ratios of the line $x - y + z - 5 =$ $0 = x - 3 y - 6$ are

• A. 3, 1, – 2
• B. 2, – 4, 1
• C. $\frac { 3 } { \sqrt { 14 } } , \frac { 1 } { \sqrt { 14 } } , \frac { - 2 } { \sqrt { 14 } }$
• D. $\frac { 2 } { \sqrt { 41 } } , \frac { - 4 } { \sqrt { 41 } } , \frac { 1 } { \sqrt { 41 } }$

Answer 1

Answer: (A)

3, 1, – 2

Answer 2

If l, m, n are direction ratios of line, then by

$A l + B m + C n = 0$

For $x - y + z - 5 = 0 , l - m + n = 0$ …..(i)

For $x - 3 y - 6 = 0 , l - 3 m + 0 n = 0$ …..(ii)

or $\frac { l } { 0 + 3 } = \frac { m } { 1 - 0 } = \frac { n } { - 3 + 1 }$ or $\frac { l } { 3 } = \frac { m } { 1 } = \frac { n } { - 2 }$

$\therefore$Direction ratios are $( 3,1 , - 2 )$.

Note : Option (3), $\left( \frac { 3 } { \sqrt { 14 } } , \frac { 1 } { \sqrt { 14 } } , - \frac { 2 } { \sqrt { 14 } } \right)$ may also be an answer but best answer is $A ( 3,1 , - 2 )$ because in (3) direction cosines are written.