At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
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
Do i use the formula u x v= (u2v3 - u3v2)i - (u1v3 - u3v1)j + (u1v2 - u2v1)k ?
Oh, you mean multiplying them all together? @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
Okay, so the second and third product would be 7(5)=35 and -3(2)=-6
Then will our simplified expression look like <-42, 35, -6> * <8, 1, -6>? @nuttyliaczar
Oh no no you want to add the products after
Dot products are scalar values, meaning they only have a magnitude, no direction
Oh, so does that mean we add -42+35+(-6)? @nuttyliaczar
Yes, that will get you your dot product between v and w
Okay so that would be -13, right? Then what do we do with r = <8, 1, -6>?
The r is irrelevant to the question, so we can ignore it. And yes it is -13
Oh! Right, I just took another look at the question. So my final answer would be just -13 @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?
Yes just -13
Im not sure about your question @nuttyliaczar I think the angle between the vectors would be 90 degrees..
I mean what would the dot product of two perpendicular vectors be?
Would it be zero? @nuttyliaczar
Im sorry, I have not really gone over this much @nuttyliaczar
Yes, because the products when added would cancel each other out
It's okay, just giving you some insight on what dot products are useful for
Thank you so much for helping me and providing me some insight, I really appreciate it! @nuttyliaczar
No problem, good luck in your future endeavours