#### Question

Define direction cosines of a directed line.

#### 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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Solution Define Direction Cosines of a Directed Line. Concept: Direction Cosines and Direction Ratios of a Line.