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Math Help - how can get anything from this?....

  1. #1
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    how can get anything from this?....

    Three forces AB and C act at, and away from, the orgin of a three-dimensional coordinate system. Force acts along the x axis and has a magnitude of 3 N; force B acts along the y axis and has a magnitude of 5 N; force C acts along the z axis and has a magnitude of 2 N. Evaluate the magnitude of the resultant force and specify the angle to the xy plane at which it acts. The resultant force and its projection both lie in a plane at an angle X to the xz plane. Find this angle between these two planes.

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    Behold, the power of SARDINES!
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    Quote Originally Posted by steph21 View Post
    Three forces AB and C act at, and away from, the orgin of a three-dimensional coordinate system. Force acts along the x axis and has a magnitude of 3 N; force B acts along the y axis and has a magnitude of 5 N; force C acts along the z axis and has a magnitude of 2 N. Evaluate the magnitude of the resultant force and specify the angle to the xy plane at which it acts. The resultant force and its projection both lie in a plane at an angle X to the xz plane. Find this angle between these two planes.





    thanx

    x
    Hello steph21,

    Lets write each of your vectors in component notation.
    F_1=3 \vec i \\\ F_2=5 \vec j \\\ F_3=2 \vec k

    Now our resultant force is the sum of all the forces.

    F_r=3\vec i+ 5 \vec j +2 \vec k

    The magnitude of the force is the vector's length

    |F_r|=\sqrt{3^2+5^2+2^2}=\sqrt{38}

    To find the angle between the vector and the xy plane lets draw a right triangle. Lets start by drawing a line from the origin to the tip of the vector, and from the tip of the vector drop a perpendicular into the xy plane.

    We know both of these distances. The length of the vector is its magnitude and the perpendicular is the z component of the vector. We can find the angle by using the \sin^{-1}\left( \frac{2}{\sqrt{38}}\right) \approx .33 rad \approx 18.9^\circ

    For the last part try to find a different triangle. Good luck.
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