# Thread: Perpendicular Vector

1. ## Perpendicular Vector

If I'm given an algebraic vector as an ordered triple (1, 2, 3) and that's it, how would I go about finding vectors that are perpendicular to this one?

I need to use the dot product.

My book didn't show examples of such a problem, so I'm not sure how to do it.

Thanks.

2. Originally Posted by NAPA55
If I'm given an algebraic vector as an ordered triple (1, 2, 3) and that's it, how would I go about finding vectors that are perpendicular to this one?

I need to use the dot product.

My book didn't show examples of such a problem, so I'm not sure how to do it.

Thanks.
let (a,b,c) be perpendicular to (1,2,3)

Since they are perpendicular their dot product must be zero

$(a,b,c) \cdot (1,2,3)=0 \to a+2b+3c=0$

now we need to solve this underdetermined system of equations.

let c=s b=t then a=-2t-3s

so we get the vector (-2t-3s,t,s)=(-2t,t,0)+(-3s,0,s)=

t(-2,1,0)+s(-3,0,1)

This is all of the vectors perpendicular to (1,2,3)

they work for all values of s and t.

I hope this helps.

Good luck.