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Three Dimensional Geometry

Question
CBSEENMA12033247
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The projection of a line segment on x, y and z-axes are respectively 12. 4 and 3. Find the length and the direction-cosines of the line segment.

Solution

Let l, m, n be the direction-cosines of the line and let the length of the line segment be r.
∵    projections of the line segment on the axis are 12, 4, 3,
∴   l r = 12, m r = 4, n r = 3
Squaring and adding, we get,
(l2 + m2 + n2) r2 = 144 + 16 + 9
∴   (1) (r)2 = 169,    ∴ r = 13
therefore                                     straight l space equals 12 over 13 comma space space straight m space equals 4 over 13 comma space straight n space equals 3 over 13
  ∴    length of the line = 13 units
and direction-cosines of line are 12 over 13 comma space 4 over 13 comma space 3 over 13. comma space

Some More Questions From Three Dimensional Geometry Chapter

If α, β, γ are the angles which a line makes with the axes, prove that sin2α + sin2 β + sin2γ = 2.

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