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Question
Define direction cosines of a directed line.
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Solution
\[\text{ The direction cosines of a directed line segment are the cosines of the direction angles of the line segment } . \]
\[ \text{ Let two points} \ A \left( x_1 , y_1 , z_1 \right) \text{ and } B \left( x_2 , y_2 , z_2 \right) \text{ define the directed line segment } AB . \]
\[\text{ The direction cosines of AB are given by }\]
\[\cos \alpha = \frac{x_2 - x_1}{d}\]
\[\cos \beta = \frac{y_2 - y_1}{d}\]
\[cos\gamma = \frac{z_2 - z_1}{d}\]
\[\text{ Here, d is the distance between A and B } .\]
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