Rotation of axes
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Direction cosines
Equations are omitted for technical reasons - download the original pdf
Let [Equation goes here - download the original pdf to see it.] be a right-handed set of Cartesian coordinate axes, and let [Equation goes here - download the original pdf to see it.] be a point. [Diagram goes here - download the original pdf to see it.] Let [Equation goes here - download the original pdf to see it.] be the direction angles between OP and the [Equation goes here - download the original pdf to see it.] axes respectively. Then [Equation goes here - download the original pdf to see it.] are called the direction cosines of the point P. [Example goes here - download the original pdf to see it.] Example (2) Show that it is impossible for a line through the origin to be inclined at angles of 60º, 30º and 45º to the x, y, z-axes respectively. [Example goes here - download the original pdf to see it.] Example (3) A line OP is inclined at the angles 75º and 45º to the Ox and Oy axes respectively. What angle does OP make with the z-axis? [Example goes here - download the original pdf to see it.]
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Contents of
Rotation of axes
1 Rotation of Axes - Introduction
2 Right and left-hand coordinates
3 Direction cosines
4 Angles between lines through the origin
5 Rotation of axes
6 The summation convention
7 Invariance with respect to a rotation of the axes
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