Question

Are the given vectors normal? a={5,-2} and b={6,15} I don't know how to find the answer. :(

Answer 1

Have you learned about dot products yet?

Answer 2

That's a x b = |a| x |b| x cos(θ), right?

Answer 3

Yeah, that's one way to write it.
Another way to compute the dot product is:
\[<x_1, y_1> ·<x_2,y_2> = x_1*x_2 + y_1*y_2\]

We're going to use both equations to check if the vectors are normal.

Answer 4

First, compute the dot product with the equation I wrote. This will give us a dot b.

Once you have that, plug it into the equation you have to find cos(theta).

Answer 5

I got 0=0 using the equation.

Answer 6

OK.
So, if the dot product is 0 from my equation that gives us:
\[0 = |a|*|b|*\cos(\theta)\]
Now, we know that this means either |a|, |b|, or cos(ϴ) is also 0.
We know that |a| and |b| aren't 0 (those vectors have to have length).
This leaves us the equation:
\[\cos(\theta) = 0\]

Answer 7

Does it make sense how I got there?

Answer 8

Yeah

Answer 9

OK. Solve that for theta. If it's 90°, then the vectors are normal (at a right angle).