# If the line is passing through the points $$(x_1, y_1, z_1)$$ and has direction cosines l, m, n of the line, then which of the following is the cartesian equation of the line?

Category: QuestionsIf the line is passing through the points $$(x_1, y_1, z_1)$$ and has direction cosines l, m, n of the line, then which of the following is the cartesian equation of the line?
Editor">Editor Staff asked 11 months ago

If the line is passing through the points $$(x_1, y_1, z_1)$$ and has direction cosines l, m, n of the line, then which of the following is the cartesian equation of the line?

(a) $$\frac{x-x_1}{l}=\frac{y-y_1}{m}=\frac{z-z_1}{n}$$

(b) $$\frac{x-x_1}{n}=\frac{y-y_1}{m}=\frac{z-z_1}{l}$$

(c) $$\frac{x+x_1}{n}=\frac{y+y_1}{m}=\frac{z-z_1}{l}$$

(d) $$\frac{x+x_1}{l}=\frac{y+y_1}{m}=\frac{z+z_1}{n}$$

The question was posed to me in an international level competition.

My question is based upon Three Dimensional Geometry in division Three Dimensional Geometry of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options
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The correct choice is (a) $$\frac{x-x_1}{l}=\frac{y-y_1}{m}=\frac{z-z_1}{n}$$
$$\frac{x-x_1}{l}=\frac{y-y_1}{m}=\frac{z-z_1}{n}$$.