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Computing the angles of Vector to x,y,z axisses

  1. Aug 28, 2012 #1
    1. The problem statement, all variables and given/known data

    A vector is given by R = 2.00 i + 1.70 j + 2.81 k.

    (a) Find the magnitudes of the x, y, and z components.
    x = 2
    y = 1.70
    z = 2.81
    (b) Find the magnitude of R.
    3.85
    (c) Find the angle between R and the x axis.
    ?
    Find the angle between R and the y axis.
    ?
    Find the angle between R and the z axis.
    ?

    3. The attempt at a solution
    I have the correct answers for part (a)& (b) but very confused on (c) what I needed to do to find angle
     
  2. jcsd
  3. Aug 28, 2012 #2
    You'll need to use the dot product. For two vectors a and b, the dot product is:

    [itex]\vec{a}\cdot\vec{b} = a_xb_x + a_yb_y + a_zb_z = |a||b|cosθ[/itex]

    You want to solve this for θ. What two vectors do you need to use to find the angle between R and the x-axis?

    Edit: Just to be clear, in the above equation, θ is the angle between a and b. You already know that you have to use R, but what other vector can you use that points along the x-axis? The y-axis? The z-axis?
     
    Last edited: Aug 28, 2012
  4. Aug 28, 2012 #3
    You are looking for the angle the displacement vector is from each axis. So for the angle from the x-axis you need to consider the displacement from the j and k components (similar to what you did in part b) and determine the corresponding angle to the triangle formed by the j/k displacement and the given i value.
     
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