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>

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- anonymous

- jamiebookeater

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- nuttyliaczar

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

- anonymous

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

- anonymous

Oh, you mean multiplying them all together? @nuttyliaczar

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## More answers

- nuttyliaczar

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

- anonymous

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

- anonymous

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

- nuttyliaczar

Oh no no you want to add the products after

- nuttyliaczar

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

- anonymous

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

- nuttyliaczar

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

- anonymous

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

- anonymous

- nuttyliaczar

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

- anonymous

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

- nuttyliaczar

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?

- nuttyliaczar

Yes just -13

- anonymous

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

- nuttyliaczar

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

- anonymous

Would it be zero? @nuttyliaczar

- anonymous

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

- nuttyliaczar

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

- nuttyliaczar

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

- anonymous

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

- nuttyliaczar

No problem, good luck in your future endeavours

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