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The two lines with the equation r=(1,2,-44)+ t(k+1, 3k+1,k-3) and x=2-3s, y=1-10s, z=3-5s, are given.
a) determine the vaulue for K when the lines are paralel
b) determine the value of K when the lines are perpendictular

  • Vector -

    Vector 1 = (K+1) i +(3K+1)j + (K-3) k
    Vector 2 = -3 i -10 j -5 k

    If those are parallel the cross product is zero
    i j k
    K+1 3K+1 K-3
    -3 -10 -5

    i term -5(3K+1) + 10(K-3) = 0
    K = -7
    same for j and k directions, K = -7

    If they are perpendicular the dot product is 0

    (K+1)(-3) +(3K+1)(-10) + (K-3)(-5) = 0
    solve for K

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