# Vector translation question

• Oct 31st 2008, 06:31 AM
woollybull
Vector translation question
If p = 2i-j+3k, q=5i+2j and r=4i+j+k, find a set of numbers f,g and h such that fp +gp +hr = 0. What does this tell you about the translations represented by p,q and r?

I thought to do this I just need to solve 3 simultaneous equations,
1. 2f + 5g +4h =0
2. -f + 2g +h =0
3. 3f + h =0

But how as I have no constant value and just solve each variable to be zero.
The book gives 1,2,-3 (or multiples of) and I can see that this is right but I dont know how to get it.
Also, what does this tell you about the translations represented by p,q and r??

Thanks.
• Oct 31st 2008, 07:51 AM
HallsofIvy
Quote:

Originally Posted by woollybull
If p = 2i-j+3k, q=5i+2j and r=4i+j+k, find a set of numbers f,g and h such that fp +gp +hr = 0. What does this tell you about the translations represented by p,q and r?

I thought to do this I just need to solve 3 simultaneous equations,
1. 2f + 5g +4h =0
2. -f + 2g +h =0
3. 3f + h =0

But how as I have no constant value and just solve each variable to be zero.
The book gives 1,2,-3 (or multiples of) and I can see that this is right but I dont know how to get it.
Also, what does this tell you about the translations represented by p,q and r??

Thanks.

I'm not sure what you mean by these as "translations" but the situation you give is precisely the definition of "independent" set of vectors. Since there are three vectors, in 3 dimensions, the fact that they are independent tells you that they form a basis for R3.

That means, I guess, that you could use those to translate from any point to any other point.
• Nov 1st 2008, 02:26 AM
woollybull
Thanks.

It made sense not long after I decided to take a break.
• Nov 1st 2008, 03:00 AM
earboth
Quote:

Originally Posted by woollybull
If p = 2i-j+3k, q=5i+2j and r=4i+j+k, find a set of numbers f,g and h such that fp +gp +hr = 0. What does this tell you about the translations represented by p,q and r?

I thought to do this I just need to solve 3 simultaneous equations,
1. 2f + 5g +4h =0
2. -f + 2g +h =0
3. 3f + h =0

But how as I have no constant value and just solve each variable to be zero.
The book gives 1,2,-3 (or multiples of) and I can see that this is right but I dont know how to get it.
Also, what does this tell you about the translations represented by p,q and r??

Thanks.

$3\cdot \vec r - 2\cdot \vec q = \vec p$
That means the vectors $\vec p, \vec q, \vec r$ are not independent and therefore they don't form a base of the $\mathbb{R}^3$