Show that `2.bar9=3`

Show that 0.3bar(56)=(353)/(990)

Show that if bar(AB)=bar(DC) , then the figure ABCD is a parallelogram.

Show that : 2/3 times 4/9 = 4/9 times 2/3

If A,B are two independent events,show that bar(A) and bar(B) are also independent.

If G is the centroid of triangleABC and O is any point in the plane of triangleABC , show that (1) bar(GA)+bar(GB)+bar(GC)=bar(0) (2) bar(OA)+bar(OB)+bar(OC)=3bar(OG) .

Show that vectors |bar(b)|bar(a)+|bar(a)|bar(b) and |b|bar(a)-|a|bar(b) are orthogonal

If bar(a),bar(b) and bar(c) are position vectors of A,B and C respectively such that 9bar(c)=4bar(a)+5bar(b) Show that A,B and C are collinear, hence find ratio in which C divides AB

bar(a),bar(b),bar(c) are three non-coplanar vectors. If bar(p)=(bar(b)xxbar(c))/(bar(a)*(bar(b)xxbar(c))),bar(q)=(bar(c)xxbar(a))/(bar(a)*(bar(b)xxbar(c))),bar(r)=(bar(a)xxbar(b))/(bar(a)*(bar(b)xxbar(c))) , show that bar(a)*bar(p)+bar(b)*bar(q)+bar(c)*bar(r)=3 .

Show that points with p.v bar(a)-2bar(b)+3bar(c ),-2bar(a)+3bar(b)-bar(c ),4bar(a)-7bar(b)+7bar(c ) are collinear. It is given that vectors bara,barb,bar c are non-coplanar.

If bar(a),bar(b),bar(c) are non - coplanar vectors, then show the vectors -bar(a)+3bar(b)-5bar(c),-bar(a)+bar(b)+bar(c) and 2bar(a)-3bar(b)+bar(c) are coplanar.