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# Solution for Define Direction Cosines of a Directed Line. - CBSE (Commerce) Class 12 - Mathematics

ConceptDirection Cosines and Direction Ratios of a Line

#### 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.
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