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Calculus

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1. a) Write the vector and parametric equations of the line through the points A(6, -1, 5) and B(-2, -3, 6).

b) Find another point on the line in (a).

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This is what I got for a)

r = 6i-j+5k + t(-8i-2j+k)

x = 6-8t
y = -1-2t
z = 5+t

I need help with b)

  • Calculus -

    a point on the line? Let t be any value, perhaps equal to say 1/2
    then
    x=6-4=2
    y=-1-1=-2
    z=5.5

  • Calculus -

    Hi bobpursley,

    I got 2 answers for a) but I'm not sure which one is correct, could you please help me determine which is correct?

    the first answer I got is posted in this question, the second answer I got is this one for part a) could you please help me

    for a) I got this instead:

    vector equation:
    [x, y, z] = [6, -1, 5] + t[-8, -2, 1]

    parametric equation:
    x=6+t(-2)
    x=6-2t

    y=-1+t(-3)
    y=-1-3t

    z=5+6t

    and because I got this for part a), it also means my part b) changes too.. so i got this:

    b) [x,y,z] = [6,-1,5] + t[-8,-2,1]
    = [6,-1,5] + 1[-8,-2,1]
    = [6,-1,5] + [-8,-2,1]
    = 6-8, -1-2, 5+1
    = (-2,-3,6)

    please let me know which one is correct.. thank you!

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