Vectors

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Vectors "v" and "w" are given by v = 5i - 2j and w = i + 3j. Find scalars r and s such that r ( v - w) = ( r + s )i - 20j.

  • Vectors -

    r(v-w)=(r+s)i-20j
    start with the i componnets.

    r(v-w) dot i=r+s

    (5ri-2rj-ri-3rj)dot i= r+s
    5r-r=r+s
    4r=s

    Now the j components
    r(v-w)dot j=-20
    -2r-3r=-20
    r=4 then s=1

    check my work, please

  • Vectors -

    WAT DO U MEAN BY DOT?

  • Correction - Vectors -

    The answer given above is incorrrect

    let v = [5,-2) and w = [1,3]
    then v-w = [4,-5]

    so we want r[4,-5] = [r+s, -20]
    then 4r = r+s and -5r = -20
    3r = s and r = 4

    then r = 4, then s = 12

    verification:
    LS = r(v-w)
    = 4[4,-5] = [16, -20]
    RS = [r+s, -20 = 16, -20 ] = LS

    My answer is correct!

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