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.

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.

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

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

If P,Q,R,S are the points (1,-1,0),(2,1,-1),(-3,2,2) and (0,-2,-1) respectively. Find the projection of PQ on RS.

The point P (3,2,4),Q(4,52),R(5,8,0) and S(2,-1,6) are :

A triangle has its vertices at P(1,-1),Q(3,4) and R(2,5). Find the equation of altitudes through P and Q and obtain the coordinate of their point of intersection.(This point is called ortho-centre of the triangle.)

A variable chord PQ of the parabola y^(2) = 4x is drawn parallel to the line y = x. If the parameters of the points P & Q on the parabola are p & q respectively, show that p + q = 2. Also show that the locus of the point of intersection of the normals at P & Q is 2x - y = 12.

Show that the points (4,7,8), (2,3,4) and (-1,-2,1),(1,2,5) are vertices of a parallelogram.