Question

The volume of the tetrahedron included between the plane

3x + 4y –5z – 60 = 0 and the coordinate planes in cubic units is

• A. 60
• B. 600
• C. 720
• D. None of these

Answer 1

Answer: (B)

600

Answer 2

Given plane meets axis at the points

A(20, 0, 0), B(0, 15, 0), C (0, 0, –12)

$\overset{\rightarrow}{OA}$= 20$\widehat{i}$, $\overset{\rightarrow}{OB}$= 15$\widehat{j}$, $\overset{\rightarrow}{OC}$= –12$\widehat{k}$

Volume =$\frac { 1 } { 6 }$ $\left| \lbrack\overset{\rightarrow}{OA}\overset{\rightarrow}{OB}\overset{\rightarrow}{OC}\rbrack \right|$= $\frac{1}{6}$× 20 × 15 × 12 = 600