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.
Short Answer TypeThe given points are A (1, – 1, 0), B (2, 1, – 1), C (– 3, 2, 2) and D (0, – 2, – 1).
Direction ratios of CD are 0 + 3, – 2 – 2, – 1 – 2 i.e.. 3, – 4, 3
∴ Direction ratios of CD are 0 + 3, – 2 – 2, – 1 – 2 i.e.. 3, – 4, 3
∴ direction cosines of CD are
(in magnitude)
The projections of a directed line segment on the co-ordinate axes are 6, -3, 2. Find its length and direction cosines.
Switch
