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 areA. B. C. D. none of these

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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