Question
The projection of a line on the co-ordinate axes are 6, 2, 3. Find the length of the line and its direction cosines. Also, find the projection of the line segment joining (2, – 3, 1) to (4, 2, 3) on this line.
Solution
Let l, m, n be the direction cosines of the line PQ and let the length of the line segment be r.
∵ projections of the line segment on the axes are 6, 2, 3.
∴ l r = 6, m r = 2, n r = 3
Squaring and adding. we get,
(l2 + m2 + n2) r2 = 36 + 4 + 9
∵ r2 = 49 ⇒ r = 7
∴ length of line = 7 units
and direction cosines of line PQ are
We are to find projection of line segment joining A (2, -3, 1) to B (4, 2, 3) on PQ
and direction cosines of line PQ are
We are to find projection of line segment joining A (2, -3, 1) to B (4, 2, 3) on PQ
