# Thread: Vector translation question

1. ## 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.

2. 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.

3. Thanks.

It made sense not long after I decided to take a break.

4. 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.
According to your result

$3\cdot \vec r - 2\cdot \vec q = \vec p$

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