Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

The equation of the plane is given as $3x-2y-q=0$.

Since the plane passes through the point $B(3,2,4)$, its coordinates must satisfy the plane equation. Substituting $x=3$ and $y=2$:

$3(3)-2(2)-q=0$

$9-4-q=0\Rightarrow q=5$

The plane also passes through the point $A(1,p,2)$. Substituting $x=1$, $y=p$, and $q=5$ into the plane equation:

$3(1)-2(p)-5=0$

$3-2p-5=0$

$-2p=2\Rightarrow p=-1$

Thus, $p=-1$ and $q=5$.

Answer: $p=-1,q=5$