Anonymous
Anonymous asked in Science & MathematicsPhysics · 9 years ago

Given u=[1 2 1], v=[-2 3 2] and w=[4 -1 3], find a scalar k such that ku+v is perpendicular to w?

having a bit of trouble understanding how i would make this perpendicular. help would be appreciated

2 Answers

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  • Anonymous
    9 years ago
    Best Answer

    m = ku+v

    m = k{1,2,1} + {-2,3,2}

    m = {k-2, 2 k+3, k+2}

    vector m perpendicular to w if

    m • w = 0

    {k-2, 2 k+3, k+2} • {4,-1,3} = 0

    5 (k-1) = 0

    k = 1

  • 9 years ago

    look multiply k with u it becomes ki + 2kj + kk and else v is -2i + 3j + 2k .... adding both of them u get (k-2)i + (2k +3)j + (k+2)k is ku + v ... similarly w = 4i -j + 3k ... as they are perpendicular ... so their dot product will be zero .... (ku+v).w = 0 .... doing this u wud get k .. dothis yourself ... and enjoy this ... i won't make your way that easy ... best of luk .. :)

    Source(s): Meee
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