Homework Help: Find a vector orthogonal

1. Sep 2, 2005

Whatupdoc

Find a vector orthogonal to both <-3,2,0> and to <0,2,2> of the form
<1,_,_> (suppose to fill in the blanks)

well i thought the cross product would do the trick, but i keep getting the wrong answer.
I|2 0| - j |-3 0| + k |-3 2|
|2 2| |0 2| |0 2|

(format is kinda messed up, but im pretty sure you can tell how i had it set up)

i(4-0) -j(-6-0)+ k(-6-0) = 4i+6j+6k = 2i+3j+6k

so the answer should be <2,3,6> which is obviously incorrectly cause i dont even have a 1.

2. Sep 2, 2005

teclo

assuming that's the correct answer, why don't you multiply by a scalar

3. Sep 2, 2005

Theoretician

You're pretty much right, apart from the sloppy sign change that crept in towards the end for no reason (-6k not +6k). Is it specified in the question that all components must be integers? If not, I would suggest simply dividing your answer by 2.

4. Sep 2, 2005

LeonhardEuler

It can't be specified that the components are all integers because there is only one unique vector that is perpendicular to two non-colinear vectors, up to constant multiples. So dividing gives the unique answer to the problem.

5. Sep 2, 2005

Theoretician

I suppose that I was being over cautious that I could have made some kind of mistake or overlooked something but you are right of course.

6. Sep 2, 2005

Whatupdoc

thanks alot, dividing by 2 worked. i had the -6 in on my paper, but when i typed it on here, everything was messed up including the answer i gave at the end. i was really sleepy awhile i was typing it, thanks agian for the help