Question

PLEASE HELP ME!!!!!!!!!!!!!
I have no idea where to start?

Evaluate the expression:

v ⋅ w

Given the vectors:

r = <8, 1, -6>; v = <6, 7, -3>; w = <-7, 5, 2>

Answer 1

Dot products are scalar products that you obtain by multiplying each of the like dimensions with each other and then adding all of the products

Answer 2

Do i use the formula u x v= (u2v3 - u3v2)i - (u1v3 - u3v1)j + (u1v2 - u2v1)k ?

Answer 3

Oh, you mean multiplying them all together? @nuttyliaczar

Answer 4

We're just looking at vectors v and w here so ignore the first. There will be three products here since both vectors have three dimensions/components. The first product is (6)(-7)=-42

Answer 5

Okay, so the second and third product would be 7(5)=35 and -3(2)=-6

Answer 6

Then will our simplified expression look like <-42, 35, -6> * <8, 1, -6>? @nuttyliaczar

Answer 7

Oh no no you want to add the products after

Answer 8

Dot products are scalar values, meaning they only have a magnitude, no direction

Answer 9

Oh, so does that mean we add -42+35+(-6)? @nuttyliaczar

Answer 10

Yes, that will get you your dot product between v and w

Answer 11

Okay so that would be -13, right? Then what do we do with r = <8, 1, -6>?

Answer 12

@nuttyliaczar

Answer 13

The r is irrelevant to the question, so we can ignore it. And yes it is -13

Answer 14

Oh! Right, I just took another look at the question. So my final answer would be just -13
@nuttyliaczar

Answer 15

And while we are on this topic, what does this dot product tell you about the vectors? For example, what would happen if you had two perpendicular vectors?

Answer 16

Yes just -13

Answer 17

Im not sure about your question @nuttyliaczar I think the angle between the vectors would be 90 degrees..

Answer 18

I mean what would the dot product of two perpendicular vectors be?

Answer 19

Would it be zero? @nuttyliaczar

Answer 20

Im sorry, I have not really gone over this much @nuttyliaczar

Answer 21

Yes, because the products when added would cancel each other out

Answer 22

It's okay, just giving you some insight on what dot products are useful for

Answer 23

Thank you so much for helping me and providing me some insight, I really appreciate it! @nuttyliaczar

Answer 24

No problem, good luck in your future endeavours