## anonymous one year ago Let u = <-6, 1>, v = <-5, 2>. Find -4u + 2v. @ganeshie8 @hero @dan815 @pooja195 @triciaal @loser66 @wio @luigi0210

1. zzr0ck3r

hint: $$-4u=\langle -4(-6),-4(1)\rangle = \langle 24, -4\rangle$$

2. anonymous

i really have no idea wow i feel dumb

3. anonymous

@zzr0ck3r

4. anonymous

5. UsukiDoll

adding vectors is in the form $u_1+v_1,u_2+v_2,...u_n+v_n$ but before we can do that we need to distribute the -4 on the u vector and distribute the 2 on the v vector.

6. anonymous

<34, -8> <14, 0> <14, 3> <44, -12> @UsukiDoll @ganeshie8 these are my options

7. UsukiDoll

zzrocker already did the distribute -4 all over the u vector now we have to distribute 2 all over the v vector 2<-5,2>

8. UsukiDoll

now what's -5 x 2 and 2 x 2

9. anonymous

-10 and 4 @UsukiDoll

10. UsukiDoll

ok cool... so our 2v is <-10,4> so let's add them together zzrocker already did -4u which was <24,-4> so now we have <24,-4> +<-10,4> $<u_1,u_2> + <v_1,v_2>$ so we have $u_1 = 24, u_2 = -4, v_1 = -10, v_2 = 4$ but our final answer has to be in the form $<u_1+v_1,u_2+v_2>$

11. anonymous

one of my option is 14,0 is that the answer?

12. anonymous

@UsukiDoll

13. UsukiDoll

u vector $<u_1,u_2...u_n>$ v vector $<v_1,v_2,...v_n>$ u+v vector $u_1+v_1,u_2+v_2+...u_n+v_n$

14. UsukiDoll

$<24-10,-4+4 >$

15. anonymous

wait so was i right? @UsukiDoll

16. UsukiDoll

yes .. 24-10 = 14 and -4+4 = 0 your u+v vector is <14,0>

17. anonymous

can u help me with another one? @UsukiDoll

18. UsukiDoll

sure

19. anonymous

Let u = <-9, 4>, v = <8, -5>. Find u - v. <-1, -1> <-13, 13> <-17, 9> <-4, -4>

20. UsukiDoll

ok this is similar to the addition vector only we are dealing with subtraction u vector $<u_1,u_2,...u_n>$ v vector $<v_1,v_2,...v_n >$ u-v vector $<u_1-v_1,u_2-v_2,....u_n-v_n>$

21. UsukiDoll

so... we just have to match labels since we're not multiplying this time.

22. anonymous

so what do i do next? can u take me step by step with numbers? @UsukiDoll

23. UsukiDoll

sure

24. UsukiDoll

let's start with the u vector u=<-9,4> recall that our u vector is in the form of $u_1,u_2,...u_n$ since there are only 2 terms in our u vector, we have something like $u=<u_1,u_2>$ Therefore, $u_1=-9,u_2 = 4$

25. UsukiDoll

similarly for the v vector v= <8,-5> there are only two terms in our v vector, so we have something like $v=<v_1,v_2>$ Therefore, $v_1 = 8,v_2=-5$

26. anonymous

so its -1 and -1 rights?

27. UsukiDoll

now we have to do subtraction, which is finding the u-v vector which is in the form $u-v=<u_1-v_1,u_2-v_2...u_n-v_n>$

28. UsukiDoll

only one of them will be -1. Recall these values $u_1=-9,u_2 = 4$ $v_1 = 8,v_2=-5$ now our u-v vector is in the form $u-v=<u_1-v_1,u_2-v_2...u_n-v_n>$ or in this situation just $u-v=<u_1-v_1,u_2-v_2>$

29. anonymous

can you help me with another ? @UsukiDoll

30. UsukiDoll

but did you get the final answer first?

31. anonymous

yes it was -1,-1 @UsukiDoll

32. anonymous

Evaluate the expression. r = <9, -7, -1>, v = <2, 2, -2>, w = <-5, -2, 6> v ⋅ w <-18, 14, -2> -26 1 <-10, -4, -12>

33. UsukiDoll

the previous answer isn't right $u-v = <-9-8, 4-(-5)>$ please try again before we can move further.

34. UsukiDoll

what's -9-8? and what's 4-(-5) (distribute the negative)

35. anonymous

-17,9

36. UsukiDoll

there we go :)

37. UsukiDoll

so for the next question we are dealing with dot product

38. UsukiDoll

$u \cdot v =<u_1v_1,u_2v_2,...u_nv_n>$

39. anonymous

i think the answer is <-10, -4, -12> @UsukiDoll

40. UsukiDoll

only it's just $v \cdot w$ where v = <2,2,-2 > and w = <-5,-2,6> yeah you're right $v_1=2,v_2=2,v_3=-2...w_1=-5,w_2=-2,w_3=6$ $v_1w_1=-10,v_2w_2=-4,v_3w_3=-12$ <-10,-4,-12>

41. anonymous

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. B = 46°, a = 12, b = 11 A = 38.3°, C = 95.7°, c = 8; A = 141.7°, C = 84.3°, c = 8 A = 51.7°, C = 82.3°, c = 8; A = 128.3°, C = 5.7°, c = 8 A = 38.3°, C = 95.7°, c = 15.2; A = 141.7°, C = 84.3°, c = 15.2 A = 51.7°, C = 82.3°, c = 15.2; A = 128.3°, C = 5.7°, c = 1.5 @UsukiDoll

42. UsukiDoll

I'm with another question atm.