How Do You Calculate Dot Products in Geometric Problems?

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CheesyPeeps
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Homework Statement


Geometry diagram: triangle ABE is equilateral with vector p along base AB and vector q along side AE, angle ABC is a right angle, and BCDE is a parallelogram with vector r along side ED.


Homework Equations


p.q+p.r

The Attempt at a Solution


I've expanded p.(q+r) to give p.q+p.r. The magnitude of p is 3, and since ABE is an equilateral triangle, the magnitude of q is also 3, right? So then p.q=9, but the answer scheme states that p.q=4.5.
I'm still pretty new to mathematics, so I'm probably missing something really obvious, but it's better to make the mistakes now than in my exam!
 

Discussion

CheesyPeeps said:

Homework Statement


Geometry diagram with vectors p, q and r: parallelogram BCDE on top of equilateral triangle ABE, with a right angle at B, vector p along AB, q along AE and r along ED.


Homework Equations


p.q+p.r

The Attempt at a Solution


I've expanded p.(q+r) to give p.q+p.r. The magnitude of p is 3, and since ABE is an equilateral triangle, the magnitude of q is also 3, right? So then p.q=9, but the answer scheme states that p.q=4.5.
I'm still pretty new to mathematics, so I'm probably missing something really obvious, but it's better to make the mistakes now than in my exam!
p.q is certainly not equal to 9.

Maybe you could start by stating the geometric definition of the dot product in Euclidean space, or ##\mathbb R^3## in this case.
Then you will be able to deduce from that the values of p.q and p.r
 
y_A said:
Maybe you could start by stating the geometric definition of the dot product in Euclidean space, or ##\mathbb R^3## in this case.
Then you will be able to deduce from that the values of p.q and p.r

Ah, I've got it now. Thanks for your help!