The position vectors of A, B,C and D are `vec a , vec b` , `vec 2a+ vec 3b` and `vec a - vec 2b` respectively. Show that `vec (DB)=3 vec b -vec a` and `vec (AC) =vec a + vec 3b`

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) .

The non-zero vectors are vec a,vec b and vec c are related by vec a= 8vec b and vec c = -7vec b . Then the angle between vec a and vec c is

The non-zero vectors are vec a,vec b and vec c are related by vec a= 8vec b and vec c = -7vec b . Then the angle between vec a and vec c is

The position vectors of four points A, B, C and D in the plane are vec(a),vec(b),vec( c ) and vec(d) . If (vec(a)-vec(d)).(vec(b)-vec( c ))=(vec(b)-vec(d)).(vec( c )-vec(a))=0 then D is a ………………is DeltaABC .

A B C D E is pentagon, prove that vec A B + vec B C + vec C D + vec D E+ vec E A = vec0 vec A B+ vec A E+ vec B C+ vec D C+ vec E D+ vec A C=3 vec A C

If the position vector of a point A is vec a + 2 vec b and vec a divides AB in the ratio 2:3 , then the position vector of B, is

Statement 1: In "Delta"A B C , vec A B+ vec A B+ vec C A=0 Statement 2: If vec O A= vec a , vec O B= vec b ,t h e n vec A B= vec a+ vec b

The position vectors of the points (1, -1) and (-2, m) are vec(a) and vec(b) respectively. If vec(a) and vec(b) are collinear then find the value of m.

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

If vec a , vec b are any two vectors, then give the geometrical interpretation of g relation | vec a+ vec b|=| vec a- vec b|