Direction Cosines and Direction Ratios — Maths STD 12 Science — Question
Gujarat BoardEnglish MediumSTD 12 ScienceMathsDirection Cosines and Direction Ratios2 Marks
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(x1, y1, z1) and (x2, y2, z2) 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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