# Two linear algebra questions - Vector geometry

ElliottG

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...

Included?

## 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...

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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.

Staff Emeritus
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!

Staff Emeritus