If `veca,vecb,vecc,vecd` be the position vectors of points A,B,C,D respectively and `vecb-veca=2(vecd-vecc)` show that the pointf intersection of the straighat lines AD and BC divides these line segments in the ratio 2:1.

veca, vecb, vecc are the position vectors of the three points A,B,C respectiveluy. The point P divides the ilne segment AB internally in the ratio 2:1 and the point Q divides the lines segment BC externally in the ratio 3:2 show that 3vec)PQ) = -veca-8vecb+9vecc .

If veca, vecb, vecc, vecd are the position vectors of points A, B, C and D , respectively referred to the same origin O such that no three of these points are collinear and veca+vecc=vecb+vecd , then prove that quadrilateral ABCD is a parallelogram.

If veca,vecb,vecc & vecd are position vector of point A,B,C and D respectively in 3-D space no three of A,B,C,D are collinnear and satisfy the relation 3veca-2vecb+vecc-2vecd=0 then

A, B, C and D have position vectors veca, vecb, vecc and vecd , repectively, such that veca-vecb = 2(vecd-vecc) . Then

veca,vecb,vecc are non zero vectors. If vecaxxvecb=vecaxxvecc and veca.vecb=veca.vecc then show that vecb=vecc .

If veca, vecb, vecc, vecd are coplanar vectors, then (vecaxxvecb)xx(veccxxvecd)=

If veca,vecb,vecc,vecd are any for vectors then (vecaxxvecb)xx(veccxxvecd) is a vector (A) perpendicular to veca,vecb,vecc,vecd (B) along the the line intersection of two planes, one containing veca,vecb and the other containing vecc,vecd . (C) equally inclined both vecaxxvecb and veccxxvecd (D) none of these

If veca, vecb, vecc are non-null non coplanar vectors, then [(veca-2vecb+vecc, vecb-2vecc+veca, vecc-2veca+vecb)]=

ABCD is parallelogram vecA, vecB, vecC and vecD are the position vectors of vecticles A, B, C, and D with respect to any origin, them: