InterviewSolution
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InterviewSolution
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What are the direction cosines of a vector equiangular with co-ordinateaxes? |
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Answer» In analytic geometry, thedirection cosines(ordirectional cosines) of a vectorare thecosinesof the angles between thevectorand the threecoordinate axes. Equivalently, they are the contributions of each component of the basis to a unitvectorin thatdirection. The direction cosines of the line make an angleαwith each of the coordinate axes. ∴l= cosα,m= cosα,n= cosα l2+m2+n2=1 ⇒ cos2α +cos2α +cos2α = 1 ⇒ 3cos2α =1 ⇒cos2α=13 ⇒cosα=±13√ Thus, the direction cosines of the line, which is equally inclined to the coordinate axes, are ±13√,±13√,and±13√ |
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