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anonymous

  • one year ago

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

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  1. zzr0ck3r
    • one year ago
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    hint: \(-4u=\langle -4(-6),-4(1)\rangle = \langle 24, -4\rangle\)

  2. anonymous
    • one year ago
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    i really have no idea wow i feel dumb

  3. anonymous
    • one year ago
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    @zzr0ck3r

  4. anonymous
    • one year ago
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    please help @zzr0ck3r

  5. UsukiDoll
    • one year ago
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    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
    • one year ago
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    <34, -8> <14, 0> <14, 3> <44, -12> @UsukiDoll @ganeshie8 these are my options

  7. UsukiDoll
    • one year ago
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    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
    • one year ago
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    now what's -5 x 2 and 2 x 2

  9. anonymous
    • one year ago
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    -10 and 4 @UsukiDoll

  10. UsukiDoll
    • one year ago
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    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 year ago
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    one of my option is 14,0 is that the answer?

  12. anonymous
    • one year ago
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    @UsukiDoll

  13. UsukiDoll
    • one year ago
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    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
    • one year ago
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    \[<24-10,-4+4 >\]

  15. anonymous
    • one year ago
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    wait so was i right? @UsukiDoll

  16. UsukiDoll
    • one year ago
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    yes .. 24-10 = 14 and -4+4 = 0 your u+v vector is <14,0>

  17. anonymous
    • one year ago
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    can u help me with another one? @UsukiDoll

  18. UsukiDoll
    • one year ago
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    sure

  19. anonymous
    • one year ago
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    Let u = <-9, 4>, v = <8, -5>. Find u - v. <-1, -1> <-13, 13> <-17, 9> <-4, -4>

  20. UsukiDoll
    • one year ago
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    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
    • one year ago
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    so... we just have to match labels since we're not multiplying this time.

  22. anonymous
    • one year ago
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    so what do i do next? can u take me step by step with numbers? @UsukiDoll

  23. UsukiDoll
    • one year ago
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    sure

  24. UsukiDoll
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    so its -1 and -1 rights?

  27. UsukiDoll
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    can you help me with another ? @UsukiDoll

  30. UsukiDoll
    • one year ago
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    but did you get the final answer first?

  31. anonymous
    • one year ago
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    yes it was -1,-1 @UsukiDoll

  32. anonymous
    • one year ago
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    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
    • one year ago
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    the previous answer isn't right \[u-v = <-9-8, 4-(-5)>\] please try again before we can move further.

  34. UsukiDoll
    • one year ago
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    what's -9-8? and what's 4-(-5) (distribute the negative)

  35. anonymous
    • one year ago
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    -17,9

  36. UsukiDoll
    • one year ago
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    there we go :)

  37. UsukiDoll
    • one year ago
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    so for the next question we are dealing with dot product

  38. UsukiDoll
    • one year ago
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    \[u \cdot v =<u_1v_1,u_2v_2,...u_nv_n> \]

  39. anonymous
    • one year ago
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    i think the answer is <-10, -4, -12> @UsukiDoll

  40. UsukiDoll
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    I'm with another question atm.

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