If the points P,Q,R,S are `(4,7,8),(-1,-2,1),(2,3,4) and (1,2,5)` respectively show that PQ and RS intersect. Also find the point of intersection.

If P,Q,R,S are (3,6,4),(2,5,2),(6,4,4,),(0,2,1) respectively find the projection of PQ on RS.

Show that the points A(6,-7,0),B(16 ,-19 ,-4),C(0,3,-6) and D(2,-5,10) are such that AB and CD intersect at the point P(1,-1,2) .

The co-ordinates of two points P and Q are (2, 6) and (-3, 5) respectively. Find : the co-ordinates of the point where PQ intersects the x-axis.

Prove that the lines through A(0,-1,-1)a n dB(4,5,1) intersects the line through C(3,9,4)a n dD(-4,4,4)dot Also, find their point of intersection.

Show that the points (2,3,4),(-1,-2,1),(5,8,7) are collinear.

Show that the points (2,3,4),(-1,-2,1),(5,8,7) are collinear.

Prove that the lines through A(0,-1,-1)a n dB(4,5,1) intersecrs the line through C(3,9,2)a n dD(-4,4,4)dot Also, find their point of intersection.

P,Q,R,S are the points (1,2,-2), (8,10,11), (1,2,3) and (3,5,7) respectively. If s denotes the projection of PQ on RS then 29s^(2) + 29 is equal to :

Using vectors show that the points A(-2,3,5), B(7,0,-1), C(-3,-2,-5) and D(3,4,7) are such that AB and CD intersect at the point P(1,2,3).

Show that the line segments joining the points (4, 7, 8), (-1, -2, 1) and (2, 3, 4), (1, 2, 5) intersect. Verify whether the four points concyclic.