Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

The equation of the plane is $6x+4y-5z=60$.

Dividing by $60$, the intercept form of the plane is $\frac{x}{10}+\frac{y}{15}+\frac{z}{-12}=1$.

The intercepts on the coordinate axes are $a=10$, $b=15$, and $c=-12$.

The volume of the tetrahedron formed by the plane and the coordinate planes is given by $V=\frac{1}{6}|abc|$.

Substituting the values, we get $V=\frac{1}{6}|10\times 15\times (-12)|=\frac{1800}{6}=300$ cubic units.

Answer: $300$