Short Answer TypeFind the projection of the line segment joining the points (1, 2, 3), (4, 3, 1) on the line with direction ratios 3, –6, –2.
A directed line segment makes angles 45° and 60° with x-axis and y-axis and an acute angle with z-axis. If P (– 1, 2, – 3) and Q (4, 3, 1) are two points in space, find the projection of PQ on the given line.
Long Answer TypeIf P, Q, R, S are the points (– 2, 3, 4), (– 4, 4, 6), (4, 3, 5), (0, 1, 2), prove by projection that PQ is perpendicular to RS.
The given points are P (– 2, 3, 4), Q (– 4, 4, 6), R (4, 3, 5) and S (0, 1, 2).
Direction ratios of RS are. 0 – 4, 1 – 3, 2 – 5 i.e., – 4, – 2, – 3
∴   direction-cosines of RS are
   
    projection of PQ on RS
                
                                  
                 
∴ PQ is perpendicular to RS.
[∵ projection of a line perpendicular to it is zero]
Short Answer TypeThe projections of a directed line segment on the co-ordinate axes are 6, -3, 2. Find its length and direction cosines.Â
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