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



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.

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