If A, B, C and D by any four points in space, prove that
`|vec(AB)xx vec(CD)+vec(BC)xx vec(AD)+vec(CA)xx vec(BD)|=4` (Area of triangle ABC)

Show that, (vec(a)-vec(b))xx(vec(a)+vec(b))=2(vec(a)xx vec(b)) .

In a regular hexagon ABCDEF, vec(AB) +vec(AC)+vec(AD)+ vec(AE) + vec(AF)=k vec(AD) then k is equal to

The position vectors of the points A, B, C are vec(a),vec(b) and vec( c ) respectively. If the points A, B, C are collinear then prove that vec(a)xx vec(b)+vec(b)xx vec( c )+vec( c )xxvec(a)=vec(0) .

(vec(a)xx vec(b))xx vec( c )=vec(a)xx(vec(b)xx vec( c )) . If vec(a)*vec( c ) ……………

vec(a) and vec(b) are any two vectors. Prove that |vec(a)+vec(b)|le|vec(a)|+|vec(b)|

Prove that [vec(a)+vec(b), vec(b)+vec( c ), vec( c )+vec(a)]=2[vec(a),vec(b),vec( c )] .

Let O, O' and G be the circumcentre, orthocentre and centroid of a Delta ABC and S be any point in the plane of the triangle. Statement -1: vec(O'A) + vec(O'B) + vec(O'C)=2vec(O'O) Statement -2: vec(SA) + vec(SB) + vec(SC) = 3 vec(SG)

If |vec(a)|=2|vec(b)|=5 and |vec(a)xx vec(b)|=8 then find vec(a).vec(b) .

If A(3,2,-4),B(4,3,-4),C(3,3,3) and D(4, 2,-3) are given then find the projection of vec(AD) on vec(AB)xx vec(AC) .