# Find a vector orthogonal

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.

Whatupdoc said:
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.

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

Whatupdoc said:
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.

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.

LeonhardEuler
Gold Member
Theoretician said:
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.
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.

LeonhardEuler said:
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.

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.

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