# Find the cartesian equation of a line passing through two points (8,-5,7) and (7,1,4).

Category: QuestionsFind the cartesian equation of a line passing through two points (8,-5,7) and (7,1,4).
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Find the cartesian equation of a line passing through two points (8,-5,7) and (7,1,4).

(a) $$\frac{x-8}{1}=\frac{y+5}{-6}=\frac{z-7}{3}$$

(b) $$\frac{2x-8}{-1}=\frac{3y+5}{6}=\frac{4z-7}{-3}$$

(c) $$\frac{x-8}{-1}=\frac{y+5}{6}=\frac{z-7}{-3}$$

(d) $$\frac{x-8}{-2}=\frac{y+5}{5}=\frac{z-7}{-7}$$

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The question is from Three Dimensional Geometry in portion Three Dimensional Geometry of Mathematics – Class 12
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Right answer is (c) $$\frac{x-8}{-1}=\frac{y+5}{6}=\frac{z-7}{-3}$$
i.e. $$(x_1,y_1,z_1)$$=(8,-5,7) and $$(x_2,y_2,z_3)$$=(7,1,4)
$$\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}=\frac{z-z_1}{z_2-z_1}$$
∴ the cartesian equation for the given line is $$\frac{x-8}{-1}=\frac{y+5}{6}=\frac{z-7}{-3}$$