Calculus

Where does the line through (1,0,1) and (3,−2,5)intersect the plane x+y+z=10?

(x, y, z) =________?

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asked by balal
  1. going from the first point to the second
    dx = 3
    dy = -2
    dz = 4
    so my line direction is 3 i -2 j + 4 k
    and my line in parametric form is
    (1,0,1) + (3, -2, 4) t

    at intersection
    x = 1+3t
    y = -2 t
    z = 1+4t
    and we know x + y + z = 10
    2 + 5 t = 10
    t = 8/5
    so
    x = 1 + 24/5 = 29/5
    y = -16/5 = -16/5
    z = 1 + 32/5 = 37/5
    Check my arithmetic !!

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    posted by Damon

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