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.

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

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 colinear and satisfy the relation 3veca-2vecb+vecc-2vecd=0 then (a) A, B, C and D are coplanar (b) The line joining the points B and D divides the line joining the point A and C in the ratio of 2:1 (c) The line joining the points A and C divides the line joining the points B and D in the ratio of 1:1 (d)The four vectors veca, vecb, vec c and vecd are linearly dependent .

If veca,vecb,vecc and vecd are unit vectors such that (vecaxxvecb)*(veccxxvecd)=1 and veca.vecc=1/2, then

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)]=

If veca,vecb,vecc are unit vectors such that veca is perpendicular to vecb and vecc and |veca+vecb+vecc|=1 then the angle between vecb and vecc is (A) pi/2 (B) pi (C) 0 (D) (2pi)/3

The line joining the points 6veca-4vecb+4vecc, -4vecc and the line joining the points -veca-2vecb-3vecc, veca+2vecb-5vecc intersect at

If veca+2vecb+3vecc, 2veca+8vecb+3vecc, 2veca+5vecb-vecc and veca-vecb-vecc be the positions vectors A,B,C and D respectively, prove that vec(AB) and vec(CD) are parallel. Is ABCD a parallelogram?