What is the vector orthogonal to <-3,2,0> and <0,2,2> with the form <1,_,_>?

[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 I am 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 don't even have a 1.

 

[teclo]

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 I am 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 don't even have a 1.

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

 

[Theoretician]

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 I am 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 don't 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]

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.

 

[Theoretician]

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.

 

[Whatupdoc]

thanks a lot, 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