## 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>

1. 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

2. anonymous

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

3. anonymous

Oh, you mean multiplying them all together? @nuttyliaczar

4. 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

5. anonymous

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

6. anonymous

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

7. nuttyliaczar

Oh no no you want to add the products after

8. nuttyliaczar

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

9. anonymous

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

10. nuttyliaczar

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

11. anonymous

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

12. anonymous

@nuttyliaczar

13. nuttyliaczar

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

14. anonymous

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

15. 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?

16. nuttyliaczar

Yes just -13

17. anonymous

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

18. nuttyliaczar

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

19. anonymous

Would it be zero? @nuttyliaczar

20. anonymous

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

21. nuttyliaczar

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

22. nuttyliaczar

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

23. anonymous

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

24. nuttyliaczar

No problem, good luck in your future endeavours