First slide

Planes in 3D

Question

The volume of the tetrahedron included between the plane $3 x + 4 y - 5 z - 60 = 0$ and the coordinate planes in cubic units is

Moderate

A

60
B

600
C

720
D

none of these

Solution

Vertices of the tetrahedron are
$(0, 0, 0), (20, 0, 0), (0, 15, 0)$ and $(0, 0, 12)$
so its volume is $\frac{1}{6} |\begin{array}{cccc} 0 & 0 & 0 & 1 \\ 20 & 0 & 0 & 1 \\ 0 & 15 & 0 & 1 \\ 0 & 0 & 12 & 1 \end{array}| ∣= 600$
cubic units.

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