Why isn't the cross product working?

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Homework Help Overview

The discussion revolves around finding a unit vector that is orthogonal to two given vectors, a = <1,2,1> and b = <1,8,1>. The original poster attempts to use the cross product to find this vector but encounters issues with the components of their result.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the use of the cross product and the definition of a unit vector. There are attempts to clarify the requirements for the resultant vector, including the need for a positive first coordinate and the implications of the unit vector definition.

Discussion Status

Participants are exploring various interpretations of the problem and discussing the necessary steps to ensure the resultant vector meets the criteria. Suggestions have been made to consider the negative of the resultant vector and to verify the definition of a unit vector.

Contextual Notes

There is an emphasis on carefully reading the problem statement, particularly regarding the requirements for the vector to be found. The original poster has expressed confusion over the expected outcome and the operations performed on the vectors.

mr_coffee
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Hello everyone, this should be a simple problem..its for matrices and I already delt with this in calc III and physics but it says:
find a unit vector with positive first coordinate orthogonal to both a and b.
a = <1,2,1>
b = < 1,8,1>
so i took the cross product and got:
<-6,0,6> it says, my j component is right but the i and k are wrong. Any ideas why?
 
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You are looking for a unit vector, check the definition of unit vector, you will see that your result does not conform. What do you need to do to make it fit the definition?
 
ohh my bad, well i tried it 2 different ways and still got it wrong... a unit vector is when u take the mangitude of the vector and then multiply 1/magnitude to the orignal vector and that's your unit vector. So I thought maybe it wants me to find the unit vector of <1,2,1> & <1,8,1> so i found the unit vector of each of them, and then tookk the cross product of each unit vector and got a wrong answer, so then i thought maybe they just want me to find the unit vector of the resultant of <1,2,1> x <1,8,1> it was also wrong...any ideas?
 
Your RESULT needs to be a unit vector. You do not necessarily get a unit vector as the result of operations on unit vectors. What can you do to make your resultant a unit vector. Also what operations can you to to get vector with the requested direction of the x component?
 
Just a thought.. try multiplying the vector by -1. <6, 0, -6> is still orthogonal to both a and b.
 
mr_coffee said:
so then i thought maybe they just want me to find the unit vector of the resultant of <1,2,1> x <1,8,1> it was also wrong...
This is what you want to do. So, what is the unit vector along (-6,0,6) ?

And once you find this vector, if it is not the required answer, check its negative as well (as suggested by hammie).
 
I think the answer in all this is: "read the problem just a LITTLE more carefully".

Especially about what kind of vector to find.

Unit vector was only one requirement.
 

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