Is the Vector Equation AxB=AxC Only True When A=0 or B=C?

Click For Summary

Homework Help Overview

The discussion revolves around the vector equation AxB = AxC, where A, B, and C are vectors. Participants are exploring the conditions under which this equation holds true and questioning the validity of a statement regarding the necessity of A being zero or B equaling C.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are examining the implications of the vector equation and discussing whether the conditions stated in the original post are sufficient or necessary. They are considering examples and reasoning about the magnitudes and angles involved in the cross products.

Discussion Status

The discussion is active, with participants providing insights and examples to clarify the conditions under which the equation holds. There is a recognition of multiple interpretations regarding the relationship between the vectors involved, and some guidance has been offered regarding the implications of the equation.

Contextual Notes

Participants are working within the constraints of vector mathematics and are questioning the assumptions related to the equality of cross products, particularly in relation to the magnitudes and angles of the vectors involved.

cp255
Messages
54
Reaction score
0
True or False, if AxB = AxC then either A=0 or B=C.

A, B, and C are vectors and I thought this statement would be true. However the answer key says it is not. Why?
 
Physics news on Phys.org
This can be explained by following example

1387076046331.jpg
 
Ok that makes sense. Now if the the magnitude of the cross product was not zero then B would have to equal C Right?
 
The magnitude of AxB is equal to the magnitude of A times the magnitude of B times the sine of the angle between the vectors A and B. If the magnitude of C is larger than the magnitude of B, but the sine of the angle between A and C is less, AxC can be equal to AxB.
 
cp255 said:
Ok that makes sense. Now if the the magnitude of the cross product was not zero then B would have to equal C Right?
Not at all. All that AxB=AxC says is that either A=0 (in which case any two vectors B and C satisfy AxB=AxC), or that the components of B and C normal to A are equal.
 
Or that since AxB=AxC is the same as AxB-AxC=Ax(B-C)=0 then A and B-C are parallel.
 
Last edited:

Similar threads

Prove area of triangle is given by cross products of the vertex vectors....
  • · Replies 6 ·
Replies
6
Views
8K
Simple Cartesian Product Proof(s)
  • · Replies 1 ·
Replies
1
Views
4K
Obtain an equation of the plane in the form ##px+qy+rz=d##
  • · Replies 5 ·
Replies
5
Views
1K
Undergrad Vector Triple Product: Are a & c Parallel or Collinear?
  • · Replies 1 ·
Replies
1
Views
2K
Really fundamental cross/dot product questions
  • · Replies 2 ·
Replies
2
Views
2K
What is the formula for the norm of a vector cross product?
  • · Replies 5 ·
Replies
5
Views
2K
How is the Gradient of a Dot Product Correctly Calculated?
  • · Replies 13 ·
Replies
13
Views
4K
Understanding Triple Scalar Product and Its Properties: Explained Simply
  • · Replies 3 ·
Replies
3
Views
3K
Vector geometry: Proof of a trapezium and cross and dot product help
  • · Replies 18 ·
Replies
18
Views
8K
Is Addition Distributive Over the Dot Product in Vector Calculations?
  • · Replies 1 ·
Replies
1
Views
1K