Vector help

  • Thread starter 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
 

Answers and Replies

574
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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.
 
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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.
 
LeonhardEuler
Gold Member
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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.
 
574
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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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