Show that the four points P,Q,R,S with position vectors `vecp,vecq,vecr,vecs` respectively such that `5vecp-2vecq+6vecr-9vecs=vec0`, are coplanar. Also find the position vector of the point of intersection of the lines PR and QS.

Show that the four points A,B,C,D with position vectors veca,vecb,vecc,vecd respectively, such that 3veca-2vecb+5vecc-6vecd=vec0 , are collinear. Also find the position vector of the point of intersection of the lines Ac and BD.

Show that the four points A,B,C,D with position vectors veca*vecb*vecc*vecd respectively, are coplanar if and only if 3veca-2vecb+vecc-2vecd=vec0 .

Find the position vector of the mid-point of the vector joining the points P(2,3,4) and Q(4,1,-2).

Four points P,Q,R and S with respective position vectors vec p , vec q , vec r and vec s are such that 5 vec p - 2vec q+ 6 vec r - 9 vec s= vec 0 . Show that the four points are coplanar and find the P.V. of the point in which the lines PQ and RS intersect.

A,B,C and D are four points with position vectors vec a , vec b , vec c and vec d respectively such that 5 vec a - 2 vec b + 6 vec c- 9 vec d= vec 0 . Show that the point A,B,C,D are coplanar and find find the P.V. of the point in which the lines AC and BD intersects.

Find the position vector of the mid point of the vector joining the points P(2,3,4), Q(4,1,-2)

Find the position vector of the mid-point of the vector joining the points P (2, 3, 4) and Q (4, 1, 2)

Find the unit vector in the direction of vector vec PQ ,P(1,2,3) and Q(5,6,7 )

Consider two points P and Q with position vectors vec(OP) = 3veca-2vecb and vec(OQ) = veca + vecb . Find the position vector of a point R which divides the line joining P and Q in the ratio 2:1, internally.