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Question: If the direction ratios of a line are \(1 , - 3,2\), then the direction cosines of the line are...

If the direction ratios of a line are 1,−3,21 , - 3,2, then the direction cosines of the line are

A

114,−314,214\frac { 1 } { \sqrt { 14 } } , \frac { - 3 } { \sqrt { 14 } } , \frac { 2 } { \sqrt { 14 } }

B

114,214,314\frac { 1 } { \sqrt { 14 } } , \frac { 2 } { \sqrt { 14 } } , \frac { 3 } { \sqrt { 14 } }

C

−114,314,−214\frac { - 1 } { \sqrt { 14 } } , \frac { 3 } { \sqrt { 14 } } , \frac { - 2 } { \sqrt { 14 } }

D

−114,−214,−314\frac { - 1 } { \sqrt { 14 } } , \frac { - 2 } { \sqrt { 14 } } , \frac { - 3 } { \sqrt { 14 } }

Answer

114,−314,214\frac { 1 } { \sqrt { 14 } } , \frac { - 3 } { \sqrt { 14 } } , \frac { 2 } { \sqrt { 14 } }

Explanation

Solution

For D'ratio (1, – 3, 2), the direction cosine will be

(11+9+4,−31+9+4,21+9+4)\left( \frac { 1 } { \sqrt { 1 + 9 + 4 } } , \frac { - 3 } { \sqrt { 1 + 9 + 4 } } , \frac { 2 } { \sqrt { 1 + 9 + 4 } } \right) ⇒(114,−314,214)\Rightarrow \left( \frac { 1 } { \sqrt { 14 } } , \frac { - 3 } { \sqrt { 14 } } , \frac { 2 } { \sqrt { 14 } } \right).