anonymous
  • anonymous
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>
Mathematics
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anonymous
  • anonymous
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>
Mathematics
jamiebookeater
  • jamiebookeater
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nuttyliaczar
  • 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
  • anonymous
Do i use the formula u x v= (u2v3 - u3v2)i - (u1v3 - u3v1)j + (u1v2 - u2v1)k ?
anonymous
  • anonymous
Oh, you mean multiplying them all together? @nuttyliaczar

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nuttyliaczar
  • 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
  • anonymous
Okay, so the second and third product would be 7(5)=35 and -3(2)=-6
anonymous
  • anonymous
Then will our simplified expression look like <-42, 35, -6> * <8, 1, -6>? @nuttyliaczar
nuttyliaczar
  • nuttyliaczar
Oh no no you want to add the products after
nuttyliaczar
  • nuttyliaczar
Dot products are scalar values, meaning they only have a magnitude, no direction
anonymous
  • anonymous
Oh, so does that mean we add -42+35+(-6)? @nuttyliaczar
nuttyliaczar
  • nuttyliaczar
Yes, that will get you your dot product between v and w
anonymous
  • anonymous
Okay so that would be -13, right? Then what do we do with r = <8, 1, -6>?
anonymous
  • anonymous
nuttyliaczar
  • nuttyliaczar
The r is irrelevant to the question, so we can ignore it. And yes it is -13
anonymous
  • anonymous
Oh! Right, I just took another look at the question. So my final answer would be just -13 @nuttyliaczar
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
  • nuttyliaczar
Yes just -13
anonymous
  • anonymous
Im not sure about your question @nuttyliaczar I think the angle between the vectors would be 90 degrees..
nuttyliaczar
  • nuttyliaczar
I mean what would the dot product of two perpendicular vectors be?
anonymous
  • anonymous
Would it be zero? @nuttyliaczar
anonymous
  • anonymous
Im sorry, I have not really gone over this much @nuttyliaczar
nuttyliaczar
  • nuttyliaczar
Yes, because the products when added would cancel each other out
nuttyliaczar
  • nuttyliaczar
It's okay, just giving you some insight on what dot products are useful for
anonymous
  • anonymous
Thank you so much for helping me and providing me some insight, I really appreciate it! @nuttyliaczar
nuttyliaczar
  • nuttyliaczar
No problem, good luck in your future endeavours

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