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3 dimensional vector problem .

  1. Jul 31, 2007 #1
    1. The problem statement, all variables and given/known data
    Given a vector R=Rx + Ry + Rz , prove that the cos a = Rz/R where a is the angle between vector Rz and R .

    2. Relevant equations
    I just don't know how to start .

    3. The attempt at a solution
  2. jcsd
  3. Jul 31, 2007 #2


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    Your notation isn't totally clear, but I'll assume you mean Rx, Ry and Rz to be perpendicular to each other. Then draw a triangle with sides R, Rz and Rx+Ry. Since Rz and Rx+Ry are perpendicular to each other this is a right triangle. And R is the hypotenuse. Now use trig.
  4. Jul 31, 2007 #3


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    Another way is to use the dot product, if you have had that in class. One definition of [itex]\vec{u}\cdot\vec{v}[/itex] is [itex]|\vec{u}||\vec{v}|cos(\theta)[/itex] where [itex]\theta[/itex] is the angle between [itex]\vec{u}[/itex] and [itex]\vec{v}[/itex]. Another, equivalent, definition is that the dot prouct of [itex]u_x\vec{i}+ u_y\vec{j}+ u_z\vec{k}[/itex] and [itex]v_x\vec{i}+ v_y\vec{j}+ v_z\vec{k}[/itex] is [itex]u_xv_x+ u_yv_y+ u_zv_z[/itex]. comparing those should give you then angle between [itex]R_x\vec{i}+ R_y\vec{j}+ R_z\vec{k}[/itex] and [itex]R_x\vec{i}[/itex].
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