In order to do this, you must first find the "cross product" of these vectors. To do that, we can use several methods. To simplify this first, I suggest you compute:
‹1, -1, 1› × ‹0, 1, 1›
You are interested in vectors orthogonal to the originals, which don't change when you scale them. Using 0,-1,1 is much easier than 6s and 7s.
So what methods are there to compute this? You can review them here (or presumably in your class notes or textbook): http://en.wikipedia.org/wiki/Cross_produ...
In addition to these methods, sometimes I like to set up: ‹1, -1, 1› • ‹a, b, c› = 0 ‹0, 1, 1› • ‹a, b, c› = 0
That is the dot product, and having these dot products equal zero guarantees orthogonality. You can convert that to:
a - b + c = 0 b + c = 0
This is two equations, three unknowns, so you can solve it with one free parameter:
b = -c a = c - b = -2c
The computation, regardless of method, yields: ‹1, -1, 1› × ‹0, 1, 1› = ‹-2, -1, 1›
The above method, solving equations, works because you'd just plug in c=1 to obtain this solution. However, it is not a unit vector. There will always be two unit vectors (if you find one, then its negative will be the other of course). To find the unit vector, we need to find the magnitude of our vector:
First you add250+250 then you add 9+9 or you could do250×9 2 times then add them together . never mind just do 250×9 2times and that will eqaul 2,250 then add 2250+ 2250and you got the answer and the answer is 4500
The meaning of g(7) is wherever you see an x in g(x) you put a 7. In this case you are being told that x = 7
So go to 7 on the x axis, go up until you hit the blue line which is g(x) and then read what it says on the y axis. It shows 4 and that is your answer.
