JEE Main 2024 (Online) 5th April Morning ShiftQuestion 1
If $A(1,-1,2)$, $B(5,7,-6)$, $C(3,4,-10)$ and $D(-1,-4,-2)$ are the vertices of a quadrilateral $ABCD$, then its area is :
Vector Algebra
Solution
The points are coplanar, and the area is $\frac12|\overrightarrow{AC}\times\overrightarrow{BD}|=\frac12|(2,5,-12)\times(-6,-11,4)|=\frac12|(-112,64,8)|=\frac12\cdot24\sqrt{29}=12\sqrt{29}$.