Answer
(a) The point $(0,0,6)$ lies in the plane $2x+3y+4z = 24$
(b) The point $(0,3,4)$ does not lie in the plane $2x+3y+4z = 24$
(c) The point $(4,4,1)$ lies in the plane $2x+3y+4z = 24$
(d) The point $(-2,6,3)$ does not lie in the plane $2x+3y+4z = 24$
Work Step by Step
We can verify if the following points lie in the plane $2x+3y+4z = 24$
(a) $(0,0,6)$
$2(0)+3(0)+4(6) = 24$
The point $(0,0,6)$ lies in the plane $2x+3y+4z = 24$
(b) $(0,3,4)$
$2(0)+3(3)+4(4) = 0+9+16 = 25$
The point $(0,3,4)$ does not lie in the plane $2x+3y+4z = 24$
(c) $(4,4,1)$
$2(4)+3(4)+4(1) = 8+12+4 = 24$
The point $(4,4,1)$ lies in the plane $2x+3y+4z = 24$
(d) $(-2,6,3)$
$2(-2)+3(6)+4(3) = -4+18+12 = 26$
The point $(-2,6,3)$ does not lie in the plane $2x+3y+4z = 24$
