What is the Equation for the Scalar and Vector Products of Two Vectors?

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Discussion Overview

The discussion revolves around the equations defining the scalar and vector products of two vectors, particularly in the context of understanding these concepts within calculus. Participants express confusion and seek clarification on the definitions and implications of these equations.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant expresses confusion about the definitions related to the scalar and vector products of vectors.
  • Another participant provides hints regarding the equations, suggesting that the scalar product can be represented as \( a \cdot b = |a| |b| \cos \theta \) and the vector product as \( |a \times b| = |a| |b| \sin \theta \).
  • There is a question about squaring the scalar product equation, leading to the expression \( |a|^2 |b|^2 \cos^2 \theta \).
  • A follow-up inquiry is made regarding the square of the vector product, indicating ongoing exploration of these mathematical relationships.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there is ongoing confusion and multiple inquiries about the definitions and implications of the equations.

Contextual Notes

Participants express uncertainty regarding the application of the equations and the relationships between the scalar and vector products, indicating a need for further clarification on these mathematical concepts.

0517
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what can be defined by the following equation?
im new to calculus, and I'm totally lost now :(

1-2.jpg
 
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welcome to pf!

hi janice! welcome to pf! :smile:

(try using | on your keyboard and the X2 icon just above the Reply box :wink:)

hint: if the angle between vectors a and b is θ, what does the equation say? :wink:
 
0517 said:
what can be defined by the following equation?
im new to calculus, and I'm totally lost now :(

1-2.jpg

I guess you need to know that:
1. (a, b) = |a| |b| cos phi
2. |a x b| = |a| |b| sin phi
 


tiny-tim said:
hi janice! welcome to pf! :smile:

(try using | on your keyboard and the X2 icon just above the Reply box :wink:)

hint: if the angle between vectors a and b is θ, what does the equation say? :wink:


urgh, good question.
i didn't know how to answer, i think I'm super blur in this topic :(
 


tiny-tim said:
hi janice! welcome to pf! :smile:

(try using | on your keyboard and the X2 icon just above the Reply box :wink:)

hint: if the angle between vectors a and b is θ, what does the equation say? :wink:


0517 said:
urgh, good question.
i didn't know how to answer, i think I'm super blur in this topic :(

a · b = |a| |b| cos θ

so the square of it = ? @@
 
0517 said:
so the square of it = ? @@

|a|2 |b|2 cos2θ

and the square of the second part is … ? :smile:​
 

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