Question

Evaluate the dot product of (2,4) and (1,-2)

Answer 1

Vectors. Do you have your book?

Answer 2

No, I left everything in my country

Answer 3

Alright. What is a vector?

Answer 4

A vector is a number that has both direction and magnitude ?

Answer 5

Exactly. A measurement that has both MAGNITUDE and DIRECTION. This is so important to understand.

Answer 6

Now, if we're taking a dot product, you're going to only have a magnitude. You will not have a direction.

Answer 7

Good so far?

Answer 8

Yes

Answer 9

So is it going to be (2*4-1*-2)

Answer 10

Now there are two ways to determine a dot product. One is more realistic. It utilizes angles and measurements. The other is coordinate based.

Answer 11

Not quite. Stick with me.

Answer 12

Okay

Answer 13

The first method is taking the magnitude of a and multiplying it by the magnitude of b. We then multiply this by the cosine of the angle between them. Store this. You will use it later. I guarantee it.

Answer 14

How do you find the magnitude

Answer 15

The second method is a bit easier. We take A's and B's x-coordinates and we multiply those together. We then take their y-coordinates and multiply them together. All we do now is add them.

Answer 16

Both methods find magnitude.

Answer 17

So what's the equation for your problem?

Answer 18

So its 2*1 + 4*-2

Answer 19

Yup yup.

Answer 20

so its -6

Answer 21

You got it. Nice work.