JEE Previous Year Question

If $\vec{a}=2\hat{i}+\hat{j}+3\hat{k}$, $\vec{b}=\hat{i}+3\hat{j}-\hat{k}$ and $\vec{c}=3\hat{i}-\hat{j}-2\hat{k}$, then the value of $\left|\begin{array}{ccc}\vec{a}\cdot \vec{a}& \vec{a}\cdot \vec{b}& \vec{a}\cdot \vec{c}\\ \vec{b}\cdot \vec{a}& \vec{b}\cdot \vec{b}& \vec{b}\cdot \vec{c}\\ \vec{c}\cdot \vec{a}& \vec{c}\cdot \vec{b}& \vec{c}\cdot \vec{c}\end{array}\right|$ is equal to

Topic: JEE PYQ

Answer: B. Full step-by-step solution below.