Two linear algebra questions - Vector geometry

AI Thread Summary
The discussion revolves around two linear algebra homework questions involving vector geometry. The original poster struggles with finding vectors that are orthogonal to given vectors and admits to having no prior examples in class. A helpful response suggests using the dot product to establish equations for the unknown vector components, leading to a system of equations. The solution involves choosing a convenient value for one component and solving for the others, with a recommendation to test different values for further understanding. The conversation emphasizes the importance of understanding vector relationships and solving systems of equations in linear algebra.
ElliottG
Messages
24
Reaction score
0

Homework Statement


[URL]http://184.154.165.18/~devilthe/uploads/1321855187.png[/URL]

Homework Equations


No idea.

The Attempt at a Solution


Alright...so really no idea what to do here...never did any examples like this in class and have scoured over my notes for 2 hours now trying to figure this out...and can't lol.

I tried finding the vector UV and then finding a vector that is orthogonal to that with no success...

Homework Statement


[URL]http://184.154.165.18/~devilthe/uploads/1321923155.png[/URL]

Homework Equations


Included?

The Attempt at a Solution


Homework Statement


Homework Equations


The Attempt at a Solution


Again, not much clue on what to do here...actually no clue at all :(

I know it sounds like I'm trying to freeload but I've already completed 7/9 of my other homework questions it's just these two that I have no idea how to do...
 
Last edited by a moderator:
Physics news on Phys.org
Have you guys covered cross products yet?
 
No we have not...I saw that on another site as an answer to this question but had no idea how they got the answer.
 
Let the vector you seek be [x1 y1 z1]
As it is perpendicular to [3 -10 4], by calculating the dot product
we can say 3.x1 -10.y1 + 4.z1 = 0
... and similarly for the second vector.

We now have 2 equations in 3 unknowns.
So let z1 be any convenient value, I chose z1 = 1.
Solve for x1 and y1.

Check that the resultant vector is perpendicular to both of the given vectors.
 
Thanks Nascent, got it!
 
Maybe then try it with z1=2, and comment on what you discover.
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
Back
Top