Question

If the plane \(2x+3y+z = 6\) cuts coordinate axes at A, B and C, then the volume of tetrahedron OABC (where O is the origin) is ......cubic units.

• A. \(30\)
• B. \(6\)
• C. \(36\)
• D. \(180\)

Hint:

Find the intercepts and use volume = one sixth of the product of the intercepts.

Answer 1

The Correct Option is B

Step 1: Use the determinant formula:
$V = \frac16\left|\det\begin{pmatrix}3 & 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 6\end{pmatrix}\right|$.

Step 2: Evaluate:
The determinant is $3 \times 2 \times 6 = 36$, so $V = \frac{36}{6} = 6$.

Final Answer:
The volume is $6$ cubic units, option (B). \[ \boxed{6} \]