Question

If a, b, c are the direction ratios of the line and l, m, n are the direction cosines of the line, then which of the following is true?

(a) \(\frac{l}{a}=\frac{m}{b}=\frac{n}{c}=μ\)

(b) \(\frac{l}{a}=\frac{m}{b}=\frac{n}{c}=μ-1\)

(c) \(\frac{l}{a}=\frac{m}{c}=\frac{n}{b}=μ\)

(d) \(\frac{l}{a}=\frac{n+1}{b}=\frac{n}{c}=μ\)

The question was posed to me in an online quiz.

I want to ask this question from Direction Cosines and Direction Ratios of a Line topic in division Three Dimensional Geometry of Mathematics – Class 12

Answer 1

Right choice is (a) \(\frac{l}{a}=\frac{m}{b}=\frac{n}{c}=μ\)

To explain: For a given line, if a, b, c are the direction ratios and l, m, n are the direction cosines of the line then

a=μl, b=μm, c=μn

Or we can say that,

\(\frac{l}{a}=\frac{m}{b}=\frac{n}{c}=μ\), where μ is a constant.