# Find a unit vector with a positive first coordinate orthogonal to both 'a' and 'b'

1. Sep 21, 2008

### samazing18

hi! i'm new to the forums, and had a question that was more calculus-related than physics. i saw another post similar to this one, but it was incomplete and i couldn't get the answer with the information on it, any chance someone could help me out?

The question is:
"Find a unit vector with a positive first coordinate that's orthogonal to both 'a' and 'b'
a=<1,8,1>
b=<1,16,1>"

the answer i got (which is only 1/3 right) was <1/8,0,-1/8>

i've tried using cross products, and then dividing by the magnitude of the cross product to get the unit vector, but only get the j variable right, and not i and k. i've also tried projecting a onto b (and visa versa) to find parallel vectors, and then trying the cross product again, but still can't seem to get the right answer. Any ideas?

2. Sep 21, 2008

### morphism

Re: Find a unit vector with a positive first coordinate orthogonal to both 'a' and 'b

The vector you get is certainly orthogonal to both a and b, but it isn't a unit vector. This leads me to believe that you made some sort of mistake when you computed/divided by the magnitude of the cross product.

3. Sep 21, 2008

### JG89

Re: Find a unit vector with a positive first coordinate orthogonal to both 'a' and 'b

I second this. I didn't do the work myself, but dividing the components of the vector by the magnitude of the vector is the correct method to use so you probably did make a mistake in your calculations.

4. Sep 21, 2008

### samazing18

Re: Find a unit vector with a positive first coordinate orthogonal to both 'a' and 'b

you're both right, and i found the error. thank's a lot