Define direction cosines of a direction line. - Vidyadip

Question

Define direction cosines of a direction line.

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Answer

The direction cosines of a direction line segment are the cosines of the direction angles of the line segment. Let two points $A(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ define the directed line segment $AB.$
The direction cosines of $AB$ are given by $\cos$
$\alpha=\frac{\text{x}_2-\text{x}_1}{\text{d}}$
$\cos\beta=\frac{\text{y}_2-\text{y}_1}{\text{d}}$
$\cos\gamma=\frac{\text{z}_2-\text{z}_1}{\text{d}}$
Here, $d$ is the distance between $A$ and $B.$

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