NIMCET 2013 — Mathematics PYQ

Step 1: Identify the given vectors

Let the three co-terminous edges be represented by vectors $\vec{a}$, $\vec{b}$, and $\vec{c}$:

• $\vec{a}=2\hat{i}-3\hat{j}+0\hat{k}$

• $\vec{b}=1\hat{i}+1\hat{j}-1\hat{k}$

• $\vec{c}=3\hat{i}+0\hat{j}-1\hat{k}$

Step 2: Apply the volume formula

The volume $V$ of a parallelepiped with co-terminous edges $\vec{a}$, $\vec{b}$, and $\vec{c}$ is given by the magnitude of their Scalar Triple Product:

This can be calculated using the determinant of the coefficients of the vectors:

Step 3: Calculate the determinant

Expanding along the first row:

The volume of the parallelepiped is $4$ cubic units.

Correct Option: 3. 4