Question

If the points $(-1,3,2),(-4,3,-2)$ and $(5,l,m)$ lie on a straight line then $l$ and $m$ are

• A. $3,10$
• B. $-3,-10$
• C. $-3,10$
• D. $3,-10$

Answer 1

The correct option is A $3,10$

equation of line passing through points, $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ is

$\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}=\frac{z-z_1}{z_2-z_1}$

first taking points, $(-1,3,2)$ and $(5,l,m)$ equation of line passing through these two points will be:

$\frac{x+1}{6}=\frac{y-3}{l-3}=\frac{z-2}{m-2}$

since all three point lies in a straight line so point $(-4,3,-2)$ will satisfy above equation,

and after solving that we will get the values of $l,m$

$l=3$ because from above two points, it is clear that line is in $x-z$ plane , no variations in $y$

for calculating $m$

$\frac{-4+1}{6}=\frac{-2-2}{m-2}$

$m=10$