Let ${v} = \begin{pmatrix} 5 \\ -3 \end{pmatrix}$ and ${w} = \begin{pmatrix} 11 \\ -2 \end{pmatrix}$. Find the area of the parallelogram with vertices ${0}$, ${v}$, ${w}$, and $v + {w}$.
What is the best way to start this?
Thanks
[Math] Find area of parallelogram with matrix vertices
matrices
Related Solutions
Spend a little time with this figure due to Solomon W. Golomb and enlightenment is not far off:
(Appeared in Mathematics Magazine, March 1985.)
To elaborate: The height is $|u|sin(\theta)$ and the height is $|v|$. Then you can find $\theta$ as $u \cdot v = |u||v|cos(\theta)$. So the area should be $A=|u||v|sin(cos^{-1}(\frac{u \cdot v}{|u||v|}))$
Also, the algebraic answer is equivalent. $|u \times v|$ would yield the same result which you calculated already.
Best Answer
Just use determinant formula - | u x w |.
P.S. - I am sorry I am new to Maths SE so doesn't know how to edit this stuff. But , I try to help if I can.