If a line has direction ratios 2, -3, 7 then find the direction cosines.

Category: QuestionsIf a line has direction ratios 2, -3, 7 then find the direction cosines.
Editor">Editor Staff asked 11 months ago

If a line has direction ratios 2, -3, 7 then find the direction cosines.
 
(a) l=\frac{2}{\sqrt{62}},m=-\frac{7}{\sqrt{62}},n=\frac{7}{\sqrt{62}}
 
(b) l=\frac{2}{\sqrt{6}},m=-\frac{3}{\sqrt{6}},n=\frac{7}{\sqrt{6}}
 
(c) l=-\frac{2}{\sqrt{62}},m=-\frac{3}{\sqrt{62}},n=-\frac{7}{\sqrt{62}}
 
(d) l=\frac{2}{\sqrt{62}},m=-\frac{3}{\sqrt{62}},n=\frac{7}{\sqrt{62}}
 
The question was posed to me in an interview for internship.
 
This question is from Direction Cosines and Direction Ratios of a Line in chapter Three Dimensional Geometry of Mathematics – Class 12
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1 Answers
Editor">Editor Staff answered 11 months ago

Right choice is (d) l=\frac{2}{\sqrt{62}},m=-\frac{3}{\sqrt{62}},n=\frac{7}{\sqrt{62}}
 
Easy explanation: For a given line, if a, b, c are the direction ratios and l, m, n are the direction cosines of the line then
 
l=±\frac{a}{\sqrt{a^2+b^2+c^2}}
 
m=±\frac{b}{\sqrt{a^2+b^2+c^2}}
 
n=±\frac{c}{\sqrt{a^2+b^2+c^2}}
 
∴l=\frac{2}{\sqrt{2^2+(-3)^2+7^2}}, \,m=-\frac{3}{\sqrt{2^2+(-3)^2+7^2}}, \,n=\frac{7}{\sqrt{2^2+(-3)^2+7^2}}
 
Hence, l=\frac{2}{\sqrt{62}}, \,m=-\frac{3}{\sqrt{62}}, \,n=\frac{7}{\sqrt{62}}.