Answer
There is no point of intersection.
Work Step by Step
$l: (x,y,z) = (3,-1,7)+r(-5,2,1)$
The x-coordinate on the line has this form: $3-5r$
The y-coordinate on the line has this form: $-1+2r$
The z-coordinate on the line has this form: $7+r$
We can find the value of $r$ such that these three coordinates satisfy the equation of the plane:
$2x+3y+4z = 24$
$2(3-5r)+3(-1+2r)+4(7+r) = 24$
$6-10r-3+6r+28+4r = 24$
$31 = 24$
Clearly this statement is a contradiction. Therefore, there is no value of $r$ such that a point on the line satisfies the equation of the plane. Therefore, there is no point of intersection.
