How Do You Calculate Dot Products in Geometric Problems?

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SUMMARY

The discussion focuses on calculating dot products in geometric problems, specifically using vectors in an equilateral triangle scenario. The user initially miscalculated the dot product of vectors p and q, assuming both had magnitudes of 3, leading to an incorrect result of 9 instead of the correct value of 4.5. The resolution involved understanding the geometric definition of the dot product in Euclidean space, which clarified the calculations for p.q and p.r.

PREREQUISITES
  • Understanding of vector magnitudes and their properties
  • Familiarity with the geometric definition of the dot product
  • Basic knowledge of Euclidean space, specifically in R³
  • Ability to manipulate and expand vector equations
NEXT STEPS
  • Study the geometric definition of the dot product in Euclidean space
  • Learn how to calculate dot products using vector components
  • Explore properties of vectors in R³, including angle and magnitude relationships
  • Practice solving problems involving dot products in geometric contexts
USEFUL FOR

Students studying mathematics, particularly those focusing on vector calculus and geometric applications, as well as educators looking to clarify concepts related to dot products.

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!
 

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