## anonymous one year ago 1.) Find a ⋅ b. a = 7i - 4j, b = 4i + 3j <28, -12> 16 -40 <11, -1> 2.)Let u = <-4, 1>, v = <-1, 6>. Find -2u + 4v. <4, 22> <4, 7> <12, -26> <10, -14>

1. princeharryyy

is that a-b

2. anonymous

@princeharryyy a times b

3. princeharryyy

the product @em2000

4. anonymous

yes

5. princeharryyy

multiply i by i and j by j

6. anonymous

i got <11, -1> for the final answer, is that what you got? @princeharryyy

7. princeharryyy

u added but we need to multiply

8. princeharryyy

try A

9. princeharryyy

what happened @em2000

10. princeharryyy

7*4 is 28 and -4*3 is -12

11. anonymous

@princeharryyy gotcha that makes sense. i got <12, -26> for #2 is that wrong?

12. princeharryyy

but before i tell you about the first and second answer, are you doing scalar vectors.

13. princeharryyy

@em2000

14. anonymous

@princeharryyy yes

15. princeharryyy

then it's my bad. the first ones answer won't be A part

16. anonymous

@princeharryyy actually im not sure, the instructions dont specify

17. princeharryyy

< and > means vectors that's why i asked

18. princeharryyy

let me tell how they work

19. princeharryyy

i.i =1, j.j =1 i.j =0 (iand j are at 90 degrees)

20. princeharryyy

|dw:1435096143456:dw|

21. princeharryyy

i, j, k are all at 90 degrees any two quantities when multiplied at 90 degrees gives 0 as i.j.cos90 =0, j.k.cos90 =0, k.i.cos90 =0

22. princeharryyy

are you getting it @em2000

23. princeharryyy

So, for the first question a = 7i - 4j, b = 4i + 3j a.b is written as a.b = (7i - 4j).(4i - 3j)

24. princeharryyy

so, a.b = 7*4*i.i -7*3*i.j -4*4*j.j-4*3j.j so, a.b = 28-0-0-12 =16 answer @em2000

25. princeharryyy

for the first question

26. princeharryyy

now for the second

27. princeharryyy

Let u = <-4, 1>, v = <-1, 6>. Find -2u + 4v. => u = -4i+1j, v = -1i+6j -2u+4v = -2(-4i+1j) +4(-1i+6j) = 8i-2j -4i+24j = 4i+22j => <4,22> answer @em2000

28. princeharryyy

which is option A @em2000 . Did you get it.

29. mathstudent55

Scalar multiplication of vectors: $$\bf{A} = \sf A_x + B_y$$ $$\bf B = \sf B_x + B_y$$ $$\bf A \cdot B \sf = A_xB_x + A_yB_y$$ Answer is scalar.

30. anonymous

@princeharryyy thank u so much

31. princeharryyy

Do you know the answers now @em2000

32. princeharryyy

for first one it is 16 and for second one i t is <4,22> @em2000

33. anonymous

@princeharryyy yes

34. princeharryyy

:)

35. mathstudent55

$$\bf A \cdot B \sf = A_xB_x + A_yB_y = (7)(4) + (-4)(3) = 28 - 12 = 16$$

36. mathstudent55

|dw:1435096919904:dw|

37. princeharryyy

thanks @mathstudent55. Sorry, for the medal she patiently tried to understand the concept. That's why I gave her the medal. Sorry, that I can't offer them to two people on one question. @em2000 could you please give a medal to @mathstudent55

38. princeharryyy

39. princeharryyy

no not to me @em2000 , but to @mathstudent55

40. mathstudent55

@princeharryyy Don't worry about the medal. I gave you one because I thought your explanation was great, and you deserved it!

41. princeharryyy

I never worry about medals @mathstudent55 but most people at open study help others for medals.