# 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}}

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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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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=&pm;\frac{a}{\sqrt{a^2+b^2+c^2}}

m=&pm;\frac{b}{\sqrt{a^2+b^2+c^2}}

n=&pm;\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}}.