Answer
$(\frac{2}{5},4,0)$
Work Step by Step
Substitute $x=\frac{t}{5}$, $y=2t$, $z=t-2$ in $10x-7y+3z+24=0$
$2t-14t+3t-6+24=0$
$18-9t=0$
$t=2$
Substitute $t=2$ in the equation of the line to get the point.
$x=\frac{2}{5}$, $y=2(2)$, $z=2-2$
$x=\frac{2}{5}$, $y=4$, $z=0$
Hence, $(\frac{2}{5},4,0)$
