Vectors and their norms

[Astaire23]

Well I'm actually struggling through this last ejercice where im asked the next:
Knowing that P,Q and R are vectors from Rⁿ and they're no nulls.
Find:
||p|| and ||q||
Knowing that:
|||R||=6
||P+Q||=√135
P=2Q+R
-3+Q.R=0
--------------------------------
By far i just found that
Q.R=3
P=2Q+R
||P||²=4||Q||²+2Q.R+||R||²
||P||²=4||Q||²+42
What should i do? Thanks for taking a look and I'll very grateful if someone can lend the name of a book or page where i can lear this better(The property of the vectors)

 

[Dr.Peterson]

It looks like you haven't yet used the fact that ||P+Q||=√135. Try doing much the same thing that you did with ||P||=||2Q+R||, and you should make progress.

 

[pka]

I wonder if the original problem is given in its entirety?
If not, please post the question as given.

 

[Astaire23]

It looks like you haven't yet used the fact that ||P+Q||=√135. Try doing much the same thing that you did with ||P||=||2Q+R||, and you should make progress.

Thanks I'll try to figure that out, maybe is applying a property that I'm not aware

 

[Astaire23]

I wonder if the original problem is given in its entirety?
If not, please post the question as given.

It's given in it's entirety, i can attach a picture but it's in Spanish, obviously mostly in math language so is understandable.

 

[Dr.Peterson]

Thanks I'll try to figure that out, maybe is applying a property that I'm not aware

As I suggested, I think you'll be doing mostly the same things you've already done, so there shouldn't be any new properties involved. If you don't get it quickly, just send us what you've done so we can see if you're going in the right direction.

It could be helpful to attach a picture of the problem, but I don't think it's essential. Here is a slight rewording of the problem as I understand it:

Suppose that P,Q, and R are vectors in Rⁿ and are not null.​

Find:​

||P|| and ||Q||​

Given that:​

||R||=6​

||P+Q||=√135​

P=2Q+R​

-3+Q.R=0​

 

[pka]

I really hoped that someone else would try this.
I think that some small bit of information has been omitted.
Please if not, show me.

 

[Dr.Peterson]

I think there is enough information here. We have to fix a minor error here:

Q.R=3
P=2Q+R
||P||²=4||Q||²+4Q.R+||R||²
||P||²=4||Q||²+48

Then we can use P=2Q+R in the form P-2Q = R, doing the same thing as above, along with squaring ||P+Q||=√135, and we can then eliminate P.Q which both resulting equations will share.

You may be right that something is missing, but I think it will work.

 

[Astaire23]

I think there is enough information here. We have to fix a minor error here:

Then we can use P=2Q+R in the form P-2Q = R, doing the same thing as above, along with squaring ||P+Q||=√135, and we can then eliminate P.Q which both resulting equations will share.

You may be right that something is missing, but I think it will work.

Thanks for the help above, i forget to tell here that i already solved the problem that way.
Knowing that P=2Q+R
||2Q+R+Q||=√135
||3Q+R||²=135
9||Q||²+6Q.R+||R||²=135
9||Q||²+18+36=135
||Q||²=81/9
||Qll=3 ←(I think that's right if not please correct me)