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

The equation of the given line can be rewritten in standard form as:

$\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-\frac{m}{2}}{\frac{3}{2}}$

From this, we can see that the line passes through the point $(4,2,\frac{m}{2})$.

Since the line lies entirely in the plane $2x-5y+2z=7$, any point on the line must satisfy the equation of the plane. Substituting the coordinates of the point into the plane's equation, we get:

$2(4)-5(2)+2\left(\frac{m}{2}\right)=7$

$8-10+m=7$

$-2+m=7$

$m=9$

Answer: 9