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Maths Homework

  1. Mar 30, 2009 #1
    1. The problem statement, all variables and given/known data
    Im stuck on a few questions i cant seem to find the methods in my notes. the questions are:

    1.The points P, Q, and R have coordinates P = (1, 0,−1),Q = (1,−2, 5) and R = (0,−3, 2).
    State which pair of points are closest to each other.
    2.A 2-dimensional force of 5[units] in the direction of the line y = 3x (upwards) acts through the
    point P = (−1,−2). Find the moment of the force about the origin.
    3.Find the solution to the differential equation below, corresponding to y(0) = 1/3
    dy/dx= 2(x − 1)2 + x cos (−x2)

    2. Relevant equations

    i dont know where to start for any of them

    3. The attempt at a solution
     
  2. jcsd
  3. Mar 30, 2009 #2
    1) do you know the formula for distance between two points?

    2) Do you know the formula for the "moment of force" (i.e. torque) about the origin?

    3) I'm assuming you mean

    [tex] \frac{dy}{dx}=2(x-1)^2 + x\cos(-x^2).[/tex]​

    If this is the case, then the first (and most important) thing to notice is whether the right-hand side (RHS) depends on just y, both x and y, or just x. Which one is it? How would this help you solve it?
     
  4. Mar 30, 2009 #3
    is the equation
    d = square root of [(x2-x1)2 + (y2-y1)2 + (z2-z1)2]
    for the 1st question?
     
  5. Mar 30, 2009 #4
    yes, it is
     
  6. Apr 1, 2009 #5
    i dont know the equation for the 2nd question
     
  7. Apr 1, 2009 #6
    Let [tex]\vec{F}[/tex] be a force with magnitude F acting at a point P, and let [tex]\vec{l}[/tex] be the displacement vector (with magnitude [tex]l[/tex]) drawn from the origin to P. Let [tex]F_\bot[/tex] be the component of [tex]\vec{F}[/tex] perpendicular to [tex]\vec{l}[/tex]. The moment of force about the origin is a vector [tex]\vec{\tau}[/tex] with magnitude

    [tex]\tau = lF_\bot[/tex]

    and direction determined by the right-hand rule with [tex]\vec{l}[/tex] as "vector one" and [tex]\vec{F}[/tex] as vector two.
     
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