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Math Help - Calc(Vectors and stuff)

  1. #1
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    Calc(Vectors and stuff)

    Here are some problems from a practice test that I couldn't get(Kept getting weird numbers), if anyone knows help would be appreciated

    1. Find a vector V tangent to graph f(x)=x^2+4x+3 at the point (2, 19)

    2. Object A is at r(t)=<t^2+3t, 7-2t, 4cos(t-2)>
    Object B is at s(t)=<5t, t^3-5, 3t-2>
    They crash at point (10, 3, 4) when t=2. What is the angle of the crash?

    3. Determine the distance from P=(9, 2, 7) to the plane x+2y+3z=6
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  2. #2
    TD!
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    1) Can you find a tangent vector? Think about the slope.
    Can you then find a perpindicular direction? (m -> -1/m).

    2) You know the dot-product, probably in two forms.
    One algebraically and one more geometrical, with cos(a) in there.
    Use both to set-up a formula for the angle between two vectors.

    3) If you've seen it, use a known formula for the point-plane distance.
    If not, find the equation of the line through the point perpindicular to the plane.
    This will intersect the plane, you don't have to find a point-point distance.
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