Three Dimension...

Direction ratios of the normal to the plane passing through the points (0, 1, 1), (1, 1, 2) and (–1, 2, – 2) are

If the length of a vector be 21 and direction ratios be 2, – 3, 6 then its direction cosines are

If the co-ordinates of the points P, Q, R, S be (1, 2, 3), (4, 5, 7), (–4, 3, – 6) and (2, 0, 2) respectively, then

The shortest distances of the point (1, 2, 3) from the axis x, y and z respectively are

If the co-ordinates of the points P and Q be (1, – 2, 1) and (2, 3, 4) and O be the origin, then

The number of straight lines that are equally inclined to the three dimensional co-ordinate axis, is

If θ is the angle between the lines AB and CD, then projection of line segment AB on line CD, is

If A(1, 2, – 1) and B(–1, 0, 1) are given, then the co-ordinates of P which divides AB externally in the ratio 1: 2 are

The point of intersection of the line joining the points (3, 4, 1) and (5, 1, 6) and the xy–plane is

If the co-ordinates of A and B be (1, 2, 3) and (7, 8, 7), then the projections of the line segment AB on the co-ordinate axis are