The area of triangle with vertices P, Q, R is given by (where $\vec{AB}$ = position vector of point B - position vector of point A)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $\frac{1}{2}|\vec{PQ}×\vec{PR}|$
$\text{Area of } \triangle PQR = \frac{1}{2} \left| \mathbf{PQ} \times \mathbf{PR} \right|$
$\mathbf{PQ} = \mathbf{Q} - \mathbf{P}$
$\mathbf{PR} = \mathbf{R} - \mathbf{P}$
Substitute the vectors:
$= \frac{1}{2} \left| (\mathbf{Q} - \mathbf{P}) \times (\mathbf{R} - \mathbf{P}) \right|$