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

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?

morphism

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.

JG89

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.

samazing18

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