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?

Category: QuestionsIf 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?
Editor">Editor Staff asked 11 months ago

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
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1 Answers
Editor">Editor Staff answered 11 months ago

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.