You must ponder the difference between a DOT product (scalar) and a CROSS product (vector). You seem a bit confused. You did half a dot product and still managed to get a vector out of it. There is a determinant in your future.
Here's the question and answer to the question my teacher has.
a. Calculate parametric equations for the line of intersection of the planes:
3x - 2y + z = 1 & 2x + y - 3z = 3.
n1 = (3, -2, 1) & n2 = (2, 1, -3) -->
vector of the line is: s = (3, -2, 1) x (2, 1, -3) = (5, 11, 7).
Now...why (5, 11, 7)? Shouldn't I multiply each component and get (6, -2, -3)?
Or is this a multiplication of two (1x3) matrices, in which case I still don't seem to get (5, 11, 7).
I am not that entirely confused because I have too much to remember and this is just a review of one of the first topics we covered in class. The review is for the final exam. If I'm not mistaken (and no I just checked and am not mistaken), a 1x3 times a 1x3 matrix is undefined. So where would the determinant be?
I found a nice formula for a cross product in my book, but don't see how I could make it a determinant. It is not in order to use a dot product here so in that case you are right TKHunny. I'll try the formula I found without using a determinant and I'll probably get the teacher's answer. I'll come back here to confirm if I get it.
Using my formula a x b = <a2b3 - a3b2, a3b1 - a1b3, a1b2 -a2b1> I also get the same answer as my teacher. Being <5, 11, 7>. It looks like the formula can be approximated to three 2 x 2 determinants but why do that when you can just plug in the values in the formula.
Looks like trying to defy the teacher in the majority of cases is not it. Although I have to admit, the students in my class have to frequently correct him for what he writes on the blackboard.