Equation of plane having intercepts −4,2 and 3 is
x
−4
+
y
2
+
z
3
=1 ⇒−3x+6y+4z=12 ⇒3x−6y−4z+12=0 Given equation of line
x−4
8
=
y−2
2
=
z−3
3
Direction ratio of line are (8,2,3) and direction ratio of plane are (3,−6,−4) ∴8×3+2×(−6)+3(−4)=0 and point 4,2,3 satisfies the plane. ∴ Line lies in the plane.