Why isn't the cross product working?

[mr_coffee]

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?

 

[Integral]

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?

 

[mr_coffee]

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?

 

[Integral]

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?

 

[Hammie]

Just a thought.. try multiplying the vector by -1. <6, 0, -6> is still orthogonal to both a and b.

 

[Gokul43201]

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).

 

[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.