Q. 115.0( 5 Votes )

The projections of a line segment on X, Y and Z axes are 12, 4 and 3 respectively. The length and direction cosines of the line segment are
A.

B.

C.

D. none of these

Answer :

If a line makes angles α , β and γ with the axes then,


cos2α + cos2β + cos2γ = 1 (1)


Let ‘r’ be the length of the line segment.


Then,


rcosα = 12, rcosβ = 4, rcosγ = 3 (2)


Now,


(rcosα)2 + (rcosβ)2 + (rcosγ)2 = 122 + 42 + 32 From (2)


r2 (cos2α + cos2β + cos2γ) = 169


r2 (1) = 169 From (1)


r


r


r = 13 (Since length cannot be negative)


Substituting r = 13 in (2) , we get


cosα , cosβ , cosγ


Thus, the direction cosines of the line are - , , .

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