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) \(\frac{x-8}{-2}=\frac{y+5}{5}=\frac{z-7}{-7}\)This question was addressed to me in an online quiz.The question is from Three Dimensional Geometry in portion Three Dimensional Geometry of Mathematics – Class 12

Find the cartesian equation of a line passing through two points (8,-5

1.	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) \(\frac{x-8}{-2}=\frac{y+5}{5}=\frac{z-7}{-7}\)This question was addressed to me in an online quiz.The question is from Three Dimensional Geometry in portion Three Dimensional Geometry of Mathematics – Class 12
Answer» Right answer is (C) \(\frac{x-8}{-1}=\frac{y+5}{6}=\frac{z-7}{-3}\) Easy explanation: CONSIDER A(8,-5,7) and B(7,1,4) i.e. \((x_1,y_1,z_1)\)=(8,-5,7) and \((x_2,y_2,z_3)\)=(7,1,4) The cartesian equation for a line passing through two points is given by \(\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}=\frac{z-z_1}{z_2-z_1}\) ∴ the cartesian equation for the given line is \(\frac{x-8}{-1}=\frac{y+5}{6}=\frac{z-7}{-3}\)

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