Area of Parallelogram

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April 21st 2008, 10:52 AM
Del

Area of Parallelogram

Find the area of the parallelogram with vertices at https://webwork.math.lsu.edu/webwork...69079f3721.png https://webwork.math.lsu.edu/webwork...ede66cc8d1.png https://webwork.math.lsu.edu/webwork...19a3d8b931.png and https://webwork.math.lsu.edu/webwork...5415e53c01.png

Area = ?

I've found the base vector multiplied by the sidw vector to be https://webwork.math.lsu.edu/webwork...fb710efe71.png, or 50.1996. I need to find the angle between these two vectors.
April 21st 2008, 11:58 AM
TheEmptySet

Quote:

Originally Posted by Del

Find the area of the parallelogram with vertices at https://webwork.math.lsu.edu/webwork...69079f3721.png https://webwork.math.lsu.edu/webwork...ede66cc8d1.png https://webwork.math.lsu.edu/webwork...19a3d8b931.png and https://webwork.math.lsu.edu/webwork...5415e53c01.png

Area = ?

I've found the base vector multiplied by the sidw vector to be https://webwork.math.lsu.edu/webwork...fb710efe71.png, 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.
April 21st 2008, 12:21 PM
Plato

If $v_1$ & $v_2$ are adjacent sides of a parallelogram then its area is $\left\| {v_1 \times v_2 } \right\|$ .
April 21st 2008, 12:28 PM
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?
April 21st 2008, 12:32 PM
Plato

Quote:

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: $v_1=3i - 5j + 0k$ .