# Thread: Area of Parallelogram

1. ## Area of Parallelogram

Find the area of the parallelogram with vertices at and

Area = ?

I've found the base vector multiplied by the sidw vector to be , or 50.1996. I need to find the angle between these two vectors.

2. Originally Posted by Del
Find the area of the parallelogram with vertices at and

Area = ?

I've found the base vector multiplied by the sidw vector to be , or 50.1996. I need to find the angle between these two vectors.
to find the angle between two vectors use the dot product

$v_1=3 \vec i -5 \vec j,v_2=-3 \vec i -11\vec j$

$v_1 \cdot v_2=|v_1||v_2|\cos(\theta)$

$-9+55=\sqrt{34} \cdot \sqrt{130} \cos(\theta)$

$\cos(\theta)=\frac{46}{\sqrt{4420}}$

Check my work as this was done while I was riding a bus without a calculator, but the theory is correct.

good luck.

3. If $v_1$ & $v_2$ are adjacent sides of a parallelogram then its area is $\left\| {v_1 \times v_2 } \right\|$.

4. Yeah, I'm trying to find the area using two adjacent sides. How do I find the cross product of two vectors on the x-y plane?

5. Originally Posted by Del
Yeah, I'm trying to find the area using two adjacent sides. How do I find the cross product of two vectors on the x-y plane?
Make the k component zero.
Example: $v_1=3i - 5j + 0k$.