Two linear algebra questions - Vector geometry

[ElliottG]

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...

 

[rootX]

Have you guys covered cross products yet?

 

[ElliottG]

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.

 

[NascentOxygen]

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.

 

[ElliottG]

Thanks Nascent, got it!

 

[NascentOxygen]

Maybe then try it with z₁=2, and comment on what you discover.