Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

The equation of the plane is $2x+3y+z=6$.

Dividing by $6$, the intercept form of the plane is $\frac{x}{3}+\frac{y}{2}+\frac{z}{6}=1$.

The intercepts on the coordinate axes are $a=3$, $b=2$, and $c=6$.

The coordinates of the vertices of the tetrahedron are $A(3,0,0)$, $B(0,2,0)$, and $C(0,0,6)$, with $O(0,0,0)$ as the origin.

The volume of the tetrahedron $OABC$ is given by $V=\frac{1}{6}abc$.

Substituting the values, $V=\frac{1}{6}(3)(2)(6)=6$ cubic units.

Answer: $6$