How do I find the area of a parallelogram with the given vertices
K (1, 3, 2) L (1, 4, 4) M (4, 9, 4) N (4, 8, 2)
I have to use the cross product, but I'm pretty lost.
Please help!
For any $\displaystyle \vec{u},\vec{v}\in\mathbb{R}^3$, $\displaystyle \|\vec{u}\times \vec{v}\|=\|\vec{u}\| \|\vec{v}\| |\sin(\vec{u},\vec{v})|$ equals the area of the parallelogram defined by the points $\displaystyle O,O+\vec{u},O+\vec{u}+\vec{v},O+\vec{v}$.
Thanks to the above, the area of $\displaystyle KLMN$ is $\displaystyle \|\overrightarrow{KL}\times\overrightarrow{KM}\|$: compute the vectors, the cross-product, and then the norm.