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VITEEE 2014 Paper

Section: Mathematics

Question : 115 of 120

Marks: +1, -0

Solution:

The given equation of the plane is 3x + 4y- 5z - 60 = 0. It can be written in the form

\frac{x}{20} + \frac{y}{15} + \frac{z}{-12}

= 1

which meets the coordinate axes at the points A(20,0,0), B(0,15,0) andC(0,0,-12). The coordinates of the origin are O (0,0,0).

Therefore, volume of the tetrahedron OABC is =

\frac{1}{6} \begin{vmatrix} 20 & 0 & 0 \\ 0 & 15 & 0 \\ 0 & 0 & -12 \end{vmatrix}

\frac{1}{6}

|20 × 15 × (-12)| = 600

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