If A, B, C are the vertices of a triangle then `vec(A)B + vec(B)C + vec(C)A =`

If A,B and C are the vertices of a triangle with position vectors vec(a) , vec(b) and vec(c ) respectively and G is the centroid of Delta ABC , then vec( GA) + vec( GB ) + vec( GC ) is equal to

If A,B and C are the vertices of a triangle with position vectors vec(a) , vec(b) and vec(c ) respectively and G is the centroid of Delta ABC , then vec( GA) + vec( GB ) + vec( GC ) is equal to

If A, B, C are the vertices of a triangle whose position vectors are vec a, vec b, vec c and G is the centroid of the triangle ABC, then vec GA + vec GB + vec GC =

If A, B, C are vertices of a triangle whose position vectors are vec a, vec b and vec c respectively and G is the centroid of Delta ABC, " then " vec(GA) + vec(GB) + vec(GC), is

If G is the centroid of Delta ABC, G' is the centroid of Delta A' B' C' then vec(A)A' + vec(B)B' + vec(C)C' =

The position vectors of the vertices A ,Ba n dC of a triangle are three unit vectors vec a , vec b ,a n d vec c , respectively. A vector vec d is such that vec d ⋅ vec a = vec d ⋅ vec b = vec d ⋅ vec c a n d vec d=lambda( vec b+ vec c)dot Then triangle A B C is a. acute angled b. obtuse angled c. right angled d. none of these

Let vec(a),vec(b),vec (c ) be the positions vectors of the vertices of a triangle , prove that the area of the triangle is 1/2| vec(a) xx vec(b) + vec(b) xx vec(c)+ vec(c)xx vec(a)|

Observe the following statements: Assertion (A) : If vertices of a triangle are A(vec(a)), B(vec(b)), C(vec(c )) , then length of altitude through A is (|vec(a) xx vec(b) + vec(b) xx vec(c)+ vec(c ) xx vec(a)|)/(|vec(b)-vec(c )|) Reason (R ): Area of triangle is Delta = (1)/(2) (Base) (Height) = (1)/(2) |vec(AB) xx vec(AC)|

A(vec a),B(vec b),C(vec c) are the vertices of the triangle ABC and R(vec r) is any point in the plane of triangle ABC ,then r*(vec a xxvec b+vec b xxvec c+vec c xxvec a) is always equal to