# Vector problems

1. Sep 9, 2010

### SOHAWONG

1.Determine if it is true that for any vectors a, b, c such that
a is not equal to 0 and a‧b = a‧ c, then b = c.

i tried to let a‧b-a‧c=0
then a‧(b-c)=0
but i found it's not meaningful
so how can i solve it =[
thz

2. Sep 9, 2010

Try to think of an example where it's not true.

3. Sep 9, 2010

### SOHAWONG

the method i have tried is really useless?

4. Sep 9, 2010

It's not useless, it just doesn't tell you anything.

You can solve this by finding a counterexample.

5. Sep 9, 2010

### SOHAWONG

assume b is not equal to c
l.h.s=a‧b
=...
should i express the dot product?

6. Sep 9, 2010

let a = (1, 0, 0), b = (1, 0, 1), c = (1, 2, 1).

What does a.(b - c) equal?

7. Sep 9, 2010

### SOHAWONG

zero =[
btw,when we want some example for conradiction,we should use some real number to think about it first?

8. Sep 9, 2010

It doesn't matter what you use.

If you're not talking about a specific set of vectors and a specific dot product, and if you assume that, for any non-zero a, and any b, c, the implication a.(b - c) = 0 ==> b = c holds (which is equivalent to a.b = a.c ==> b = c) then it doesn't matter which vector space and dot product you chose to construct your counterexample.

So, we found an example where a.(b - c) = 0, when b doesn't equal c.

9. Sep 9, 2010

### SOHAWONG

a.(b - c) = 0, when b doesn't equal c
this i'd thought once,but dunno how to express
anyway thank you very much :p