Question

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

Answer 1

Yay! Dot products are easy! :)

Answer 2

All you have to do is multiply the first number with the first number, and the second number with the second number. Then, add together. It sounds complicated in words, but when you do it with the numbers it's simple.

For example, if I want to find the dot product of (1,3) and (4,5) I would just do:
(1)(4) + (3)(5)
= 4 + 15
= 19.

Answer 3

thats it

Answer 4

For your question, we have (2,4) and (1,-2). To find the dot product we just do:
(2)(1) + (4)(-2)
= 2 - 8
= -6

Answer 5

And that's it, the dot product of (2,4) and (1,-2) is -6.

Answer 6

Does that make sense? Any questions? :)

Answer 7

yea

Answer 8

Cool!

Answer 9

The "cross" product is a little more complicated. But the "dot" product is easy.

Answer 10

what about a projection

Answer 11

Projection uses the dot product and the length of the coordinate (or vector). An extra step or two, but the same "math difficulty"

Answer 12

so (2,5) onto (1,3)
would be sovled how

Answer 13

OK, I like drawing a picture to get an idea of what is even happening.

Answer 14

lol, after drawing it I change my mind, the picture confused me more. I'll just use the formula. :)

Answer 15

it has the answers of 0.5(1,3)
1.7(1,3)
1.7(2,5)
0.5(1,3)

Answer 16

what is th eforumla

Answer 17

Alright, so the formula is: let a = (x1,y1) and b = (x2,y2)

projection of b onto a = (a dot b)/(a dot a) x a

Answer 18

where the "x a" means normal multiplication with a

Answer 19

All you need to worry about is finding (a dot b) and (a dot a)

Answer 20

Let's call a = (1,3) and b (2,5). Since the formula is project b onto a. We want to project (2,5) onto (1,3).

Answer 21

a dot b = (1,3) dot (2,5) = (1)(2) + (3)(5) =
a dot a = (1,3) dot (1,3) = (1)(1) + (3)(3) =

Answer 22

a dot b = 17
a dot a = 10

any questions so far? Sometimes the notation can freak you out. :)

Answer 23

no i am good

Answer 24

If you've got all that, then the formula just says you divide (a dot b)/(a dot a) = 17/10 = 1.7

and then multiply that by a. The final answer would then be
1.7a = 1.7 (1,3) remember that we are calling a = (1,3)

Answer 25

Alright, so a lot more than "one or two extra steps" (I lied), but not THAT big of a math deal... lol

Answer 26

i think i got it

Answer 27

yea i got it

Answer 28

Cool cool, if you have any other questions let us know. Good luck!