Solving for Vectors a, b, and c - Help Appreciated

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Discussion Overview

The discussion revolves around finding nonzero vectors a, b, and c such that the cross product a x b equals a x c, while ensuring that b does not equal c. The scope includes mathematical reasoning and vector operations.

Discussion Character

  • Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant asks for guidance on finding vectors a, b, and c that meet the specified conditions.
  • Another participant suggests that the cross product is zero for perpendicular vectors, citing Cartesian unit vectors as a potential solution.
  • A subsequent reply corrects the previous claim, stating that the dot product is zero for perpendicular vectors and clarifying that the cross product of i and j is k.
  • Another participant acknowledges the error in the previous statements, noting that the cross product is zero for parallel vectors and provides an example of vectors that satisfy the condition.
  • A later reply proposes that c can be expressed as c = b + ka, where k is a nonzero scalar, indicating that c - b is parallel to a.

Areas of Agreement / Disagreement

Participants express disagreement regarding the properties of the cross product and its application to the problem. The discussion remains unresolved with multiple competing views on how to approach the solution.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about vector properties and the conditions under which the cross product is zero. Some mathematical steps and definitions are not fully clarified.

Giuseppe
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Hello, can anyone guide me with this problem?

Find nonzero vectors a ,b , and c such that a x b = a x c but b does not equal c

I would appreciate any help. Thanks
 
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The cross product is zero for perpendicular vectors so the cartesian unit vectors would satisfy that as i x j = i x k =0.
 
inha said:
The cross product is zero for perpendicular vectors so the cartesian unit vectors would satisfy that as i x j = i x k =0.

That's all wrong. The dot product is zero for perpendicular vectors.
The cross product is i x j = k.
 
Antiphon said:
That's all wrong. The dot product is zero for perpendicular vectors.
The cross product is i x j = k.
Yeah, the cross product is zero for parallel vectors. So (1,1,1) x (2,2,2)= (1,1,1) x (3,3,3) = (0,0,0) is a solution.
 
Oh hell. I got my products mixed. Scratch that advice and sorry if I caused any problems.
 
We just need that c=b+ka so that c-b is parallel to a
(a,b,b+ka) satisfies the prop(k is a scalar not equal to zero)
 

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