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anonymous
 one year ago
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>
anonymous
 one year ago
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>

This Question is Closed

nuttyliaczar
 one year ago
Best ResponseYou've already chosen the best response.2Dot 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
 one year ago
Best ResponseYou've already chosen the best response.0Do i use the formula u x v= (u2v3  u3v2)i  (u1v3  u3v1)j + (u1v2  u2v1)k ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh, you mean multiplying them all together? @nuttyliaczar

nuttyliaczar
 one year ago
Best ResponseYou've already chosen the best response.2We'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
 one year ago
Best ResponseYou've already chosen the best response.0Okay, so the second and third product would be 7(5)=35 and 3(2)=6

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Then will our simplified expression look like <42, 35, 6> * <8, 1, 6>? @nuttyliaczar

nuttyliaczar
 one year ago
Best ResponseYou've already chosen the best response.2Oh no no you want to add the products after

nuttyliaczar
 one year ago
Best ResponseYou've already chosen the best response.2Dot products are scalar values, meaning they only have a magnitude, no direction

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh, so does that mean we add 42+35+(6)? @nuttyliaczar

nuttyliaczar
 one year ago
Best ResponseYou've already chosen the best response.2Yes, that will get you your dot product between v and w

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay so that would be 13, right? Then what do we do with r = <8, 1, 6>?

nuttyliaczar
 one year ago
Best ResponseYou've already chosen the best response.2The r is irrelevant to the question, so we can ignore it. And yes it is 13

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh! Right, I just took another look at the question. So my final answer would be just 13 @nuttyliaczar

nuttyliaczar
 one year ago
Best ResponseYou've already chosen the best response.2And 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?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Im not sure about your question @nuttyliaczar I think the angle between the vectors would be 90 degrees..

nuttyliaczar
 one year ago
Best ResponseYou've already chosen the best response.2I mean what would the dot product of two perpendicular vectors be?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Would it be zero? @nuttyliaczar

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Im sorry, I have not really gone over this much @nuttyliaczar

nuttyliaczar
 one year ago
Best ResponseYou've already chosen the best response.2Yes, because the products when added would cancel each other out

nuttyliaczar
 one year ago
Best ResponseYou've already chosen the best response.2It's okay, just giving you some insight on what dot products are useful for

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you so much for helping me and providing me some insight, I really appreciate it! @nuttyliaczar

nuttyliaczar
 one year ago
Best ResponseYou've already chosen the best response.2No problem, good luck in your future endeavours
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