How do vectors multiply

How do vectors multiply

Such as a
(1 2)
b(1 3)
a*b=(1+6)=7
That is, (x1 Y1) (x2 Y2) = x1x2 + y1y2

If a = (2,3), B = (- 1, - 2), C = (2,1), then (a dot by B) dot by C equals?
The answer is (- 16, - 8) and (- 6, - 12). How can I break these two numbers?

Vector x = (a, b), y = (C, d)
Then x dot times y = AC + BD
The first one is right, the second one should be (- 8, - 12)

If two vectors are collinear, what does that mean? Is subtraction or multiplication equal to zero?

M (x, y) n (a, b) m, n are collinear; ax + by = 0

Is it true that if two vectors are vertical and only if they are vertical, the multiplication of two vectors equals zero

If two vectors are vertical and only if they are vertical, the multiplication of two vectors equals zero