# Why isn't the cross product working?

1. Nov 4, 2005

### 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?

2. Nov 4, 2005

### Integral

Staff Emeritus
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?

3. Nov 4, 2005

### 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 thats 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?

4. Nov 4, 2005

### Integral

Staff Emeritus
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?

5. Nov 4, 2005

### Hammie

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

6. Nov 4, 2005

### Gokul43201

Staff Emeritus
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).

7. Nov 5, 2005

### 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.