The position vectors of four points P,Q,R annd S are 2a+4c,5a+`3sqrt(3)b+4c,-2sqrt(3)b+c and 2a+c` respectively, prove that PQ is parallel to RS.

If the position vectors of the points A,B and C be a,b and 3a-2b respectively, then prove that the points A,B and C are collinear.

The position vectors of the points A,B and C are hati+2hatj-hatk,hati+hatj+hatk and 2hati+3hatj+2hatk , respectively. If A is chosen as the origin, then the position vectors of B and C are

The position vectors of A,B,C are 2hati+hatj-hatk,3hati-2hatj+hatk and hati+4hatj-3hatk respectively. Show that A, B and C are collinear.

If 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.

Sum of the first p, q and r terms of an A.P. are a, b and c, respectively. Prove that a/p(q-r)+b/q(r-p)+c/r(p-q)=0

If a and b are position vector of two points A,B and C divides AB in ratio 2:1, then position vector of C is

If veca=-2hati+3hatj+5hatk,vecb=hati+2hatj+3hatkandvecc=7hati-hatk are position vectors of three points A, B, C respectively, prove that A, B, C are collinear.

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