How Do You Calculate Dot Products in Geometric Problems?

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CheesyPeeps
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Homework Statement


9uc4zs.jpg


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!
 

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CheesyPeeps said:

Homework Statement


9uc4zs.jpg


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!