Question

Find all vectors <1, a, b> orthogonal to <4, -8, 2>. Let a and b be real numbers.

Answer 1

work the dot product, what do we know about the dot product of othrogonal vectors?

Answer 2

If the angle between two vectors is 90 degrees, then their dot product will equal zero.

Answer 3

good, so lets try that

Answer 4

<1, a, b>
dot <4, -8, 2>
------------
4-8a+2b = 0

solve a in terms of b, or b in terms of a

Answer 5

Oh! Ok thats so simple, the a and b variables were throwing me off

Answer 6

or, we could find a set of a,b that fit and define a plane ... maybe

Answer 7

<1, a, 4a-2> would be a solution, right??

Answer 8

yes, at least to me thats a fair representation

Answer 9

thank you!

Answer 10

your welcomme