Vector type proof

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randayabara - 19 Oct 2008 01:27 GMT

Hi - any help would be greatly appreciated

Question:

Four vectors a; b; c and x satisfy the relation: (a . x)b = c + x.

Show that (b . a . 1)a . x = c . a

and if b . a <> 1 then express the vector x in terms of the vectors a; b
and c.

I have shown that (b . a . 1)a . x = c . a

However, the last part seems to simply involve solving (b . a . 1)a . x = c
. a for x

That seems to easy... do I have the right idea or am I mis-understanding
something?

Thanks

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[Mr.] Lynn Kurtz - 19 Oct 2008 02:31 GMT

>Hi - any help would be greatly appreciated
>
[quoted text clipped - 3 lines]
>
>Show that (b . a . 1)a . x = c . a

Does b.a mean the dot product of b and a? If so, what does a.1 mean,
and if not what does a.b mean?

--Lynn

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randayabara - 20 Oct 2008 15:56 GMT

Hi,

Yes, b.a means dot product of b and a; I'm not sure what a.1 means.

Thanks for looking into this for me :-)

R.

>>Hi - any help would be greatly appreciated
>>
[quoted text clipped - 8 lines]
>
> --Lynn

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Peter Webb - 03 Nov 2008 01:20 GMT

> Hi,
>
> Yes, b.a means dot product of b and a; I'm not sure what a.1 means.
>
> Thanks for looking into this for me :-)

I assume "1" means the vector (1,0,0,0...). You should therefore be able to
find a.1 using the rules for dot product. You should already know that
a.(1,0,0..), a.(0,1,0..), a.(0,0,1...) all have simple geometric
interpretations; if not, this is the time to find out ....

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Math Forum / Mathematics / Undergraduate Math / November 2008

Vector type proof