| ES-20 Vector Resolution in Three Dimensions |
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A vector in three dimensions may be defined in terms of the angle it makes with the vertical (y) axis and the angle a vertical plane passed through it makes with the x-axis. These angles are known as the Euler angles. |
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The y component, Ay, and the component in the x-y plane,
Ah, may be found as shown here.
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This is shown graphically.
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The horizontal component, Ah, may be broken into x and z components. |
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This is shown graphically. |
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The reverse, given a vector in Cartesian components to find the magnitude and orientation in space, may also be performed. For example, consider the diagram here. |
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The magnitude and direction can be determined as shown here. |