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

In summary, the vector orthogonal to both <-3,2,0> and <0,2,2> of the form <1,_,_> is <1, 3/2, 3>. The cross product method was initially used but resulted in an incorrect answer. Dividing the resulting vector by 2 gave the correct and unique solution to the problem.
  • #1
Whatupdoc
99
0
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.
 
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  • #2
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 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
 
  • #3
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 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.
 
  • #4
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.
 
  • #5
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.
 
  • #6
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
 

1. What is a vector orthogonal?

A vector orthogonal, also known as a perpendicular vector, is a vector that forms a right angle (90 degrees) with another vector. This means that the dot product of the two vectors is equal to 0.

2. How do I find a vector that is orthogonal to a given vector?

To find a vector that is orthogonal to a given vector, you can use the cross product. The cross product of two vectors will result in a vector that is perpendicular to both of the original vectors. You can also use the dot product to check if the vectors are orthogonal.

3. Can a vector be orthogonal to more than one vector?

Yes, a vector can be orthogonal to more than one vector. If a vector is orthogonal to a plane, it will also be orthogonal to any vector that lies in that plane.

4. Is the zero vector orthogonal to all other vectors?

No, the zero vector is not orthogonal to all other vectors. In fact, the zero vector is orthogonal only to itself. This is because the dot product of the zero vector with any other vector will always be 0.

5. Are orthogonal vectors always perpendicular in all dimensions?

Yes, orthogonal vectors are always perpendicular in all dimensions. This is because the concept of orthogonality is not limited to just two or three dimensions, but can be extended to any number of dimensions. The dot product of orthogonal vectors will always be 0, regardless of the number of dimensions.

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