Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

For the line $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-m}{2}$ to lie in the plane $2x-4y+z=7$, every point on the line must satisfy the equation of the plane.

A general point on the line can be written as $(t+4,t+2,2t+m)$.

Substituting this point into the equation of the plane, we get:

$2(t+4)-4(t+2)+(2t+m)=7$

$2t+8-4t-8+2t+m=7$

$(2-4+2)t+(8-8+m)=7$

$0\cdot t+m=7$

$m=7$

Answer: 7