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Math Help - Vector Calculus

  1. #1
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    Vector Calculus

    Show that the line r = r0 + tv is consistent with the Cartesian form
    y = mx + c.

    Confirm that the line passing through the points rA and rB can be written in the form r = trA + (1 - t)rB
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  2. #2
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    Quote Originally Posted by njr008 View Post
    Show that the line r = r0 + tv is consistent with the Cartesian form
    y = mx + c.

    Confirm that the line passing through the points rA and rB can be written in the form r = trA + (1 - t)rB
    Let v be the vector ai + bj.

    r = r0 + tv has parametric equations:

    x = x0 + at => (x - x0)/a = t .... (1)

    y = y0 + bt => (y - y0)/b = t .... (2)

    Equate (1) and (2): (x - x0)/a = (y - y0)/b.

    You should try the second one again now.

    Re-arrange into y = mx + c form.
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