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The projections of a line segment PQ on the x, y and z axes are 12,4,3 , respectively. Find | PQ| and the direction cosines of the line PQ

The projections of a line segment PQ on the x, y and z axes are 12,4,3 , respectively. Find | PQ| and the direction cosines of the line PQ

Grade:12

1 Answers

Ritesh Khatri
76 Points
6 years ago
Formula for length of a segment is
|PQ| = \sqrt{x^{2}+y^{2}+z^{2}}
=\sqrt{12^{2}+4^{2}+3^{2}}
=13
Direction cosines,
 
Below are formula for direction cosines
 l = \frac{x}{\sqrt{x^{2}+y^{2}+z^{2}}}
=12/13
m = \frac{y}{\sqrt{x^{2}+y^{2}+z^{2}}}
=4/13
n = \frac{z}{\sqrt{x^{2}+y^{2}+z^{2}}}
=3/13

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