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प्रश्न
Find the direction cosines of a line which makes equal angles with the coordinate axes.
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उत्तर
Suppose the line makes an angle a with the directrixes, then their direction cosines:
I = cos α, m = cos α, n = cos α
We know that, l2 + m2 + n2 = 1
cos2 α + cos2 α + cos2 α = 1
3cos2 α = 1
cos2 α = `1/3`
cos α = `± 1/sqrt3`
direction cosines of a line = `< 1/sqrt3, 1/sqrt3, 1/sqrt3 >` and `<-1/sqrt3, -1/sqrt3, -1/sqrt3>`
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संबंधित प्रश्न
Which of the following represents direction cosines of the line :
(a)`0,1/sqrt2,1/2`
(b)`0,-sqrt3/2,1/sqrt2`
(c)`0,sqrt3/2,1/2`
(d)`1/2,1/2,1/2`
If a line makes angles 90°, 135°, 45° with the X, Y, and Z axes respectively, then its direction cosines are _______.
(A) `0,1/sqrt2,-1/sqrt2`
(B) `0,-1/sqrt2,-1/sqrt2`
(C) `1,1/sqrt2,1/sqrt2`
(D) `0,-1/sqrt2,1/sqrt2`
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