axb=2axc

b-2c=a

given that |a|=|c|=1 and |b|=4

and the angle betweenbandcis

show that

For each of these cases find the cosine of the angle betweenaandc.

I don't know where to begin

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- Jul 5th 2010, 12:44 AMarzeCross and dot product vectors
**a**x**b**=2**a**x**c**

**b-2c**=**a**

given that |**a**|=|**c**|=1 and |**b**|=4

and the angle between**b**and**c**is

show that

For each of these cases find the cosine of the angle between**a**and**c**.

I don't know where to begin - Jul 5th 2010, 02:50 AMSwlabr
I suppose your first step would be to work out what to do with the arccos. So, where should that go? What does this tell you?

Secondly, you should work out that , and so that means the second proposition makes sense - the vectors are in the same direction. That is to say, they only differ by a scalar.

What you now want to do is prove that (why?). So, work out what is, and you will be done (why?)! (You will need the information you gleamed from my first line here).

Does that make sense? - Jul 5th 2010, 03:11 AMarze
I'm not sure I exactly understand. Cross products have the sin value multiplied by the magnitudes, right? So that's confusing me. I did work out and so and is a scalar. Ok, I understand why , since . I don't get the last one about .

Thanks! - Jul 5th 2010, 03:17 AMSwlabr
- Jul 5th 2010, 03:55 PMarze

I'm still doing something wrong. - Jul 5th 2010, 04:01 PMPlato
- Jul 5th 2010, 04:04 PMarze