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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