Question

The point of intersection of the lines $\frac { x + 3 } { - 36 } = \frac { y - 3 } { 2 } = \frac { z - 6 } { 4 }$ is

• A.
• B. $( 2,10,4 )$
• C. $( - 3,3,6 )$
• D. $( 5,7 , - 2 )$

Answer 1

Answer: (A)

Answer 2

Given lines are, $\frac { x - 5 } { 3 } = \frac { y - 7 } { - 1 } = \frac { z + 2 } { 1 } = r _ { 1 }$, (say)

and $\frac { x + 3 } { - 36 } = \frac { y - 3 } { 2 } = \frac { z - 6 } { 4 } = r _ { 2 }$ , (say)

$\therefore$ $x = 3 r _ { 1 } + 5 = - 36 r _ { 2 } - 3$, $y = - r _ { 1 } + 7 = 3 + 2 r _ { 2 }$ and

$z = r _ { 1 } - 2 = 4 r _ { 2 } + 6$

On solving, we get $x = 21 , y = \frac { 5 } { 3 } , z = \frac { 10 } { 3 }$ .

Trick: Check through options.