Prove that `3vec(OD)+vec(DA)+vec(DB)+vec(DC)` is equal to `vec(OA)+vec(OB)+vec(OC)`.

Prove that ( vec(A) + vec(B)) xx ( vec(A) - vec(B)) = 2 (vec(B) xx vec(A))

Prove that vec(a)[(vec(b) + vec(c)) xx (vec(a) + 3vec(b) + 4vec(c))] = [ vec(a) vec(b) vec(c)]

Prove that vec(a). {(vec(b) + vec(c)) xx (vec(a) + 2vec(b) + 3vec(c))} = [vec(a) vec(b) vec(c)] .

if A,B,C,D and E are five coplanar points, then vec(DA) + vec( DB) + vec(DC ) + vec( AE) + vec( BE) + vec( CE) is equal to :

If vec ba n d vec c are two-noncollinear vectors such that vec a||( vec bxx vec c), then prove that ( vec axx vec b) . ( vec axx vec c) is equal to | vec a|^2( vec bdot vec c)dot

If vec a= vec b+ vec c , vec b X vecd= vec0 and vec c*vec d=0 then ( vec dx( vec ax vec d))/( vec d^2) is equal to (a) vec a (b) vec b (c) vec c (d) vec d

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)

( vec a+2 vec b- vec c)dot{( vec a- vec b)xx( vec a- vec b- vec c)} is equal to [ vec a\ vec b\ vec c] b. c. 2[ vec a\ vec b\ vec c] d. 3[ vec a\ vec b\ vec c]

If | vec a|=2,| vec b|=5a n d vec adot vec b=0, then vec a x ( vec ax( vec ax( vec ax( vec a x( vec ax vec b))))) is equal to 64 vec a (b) 64 vec b (c) -64 vec b (d) -64 vec a

The vector (vec(a)+3vec(b)) is perpendicular to (7 vec(a)-5vec(b)) and (vec(a)-4vec(b)) is perpendicular to (7vec(a)-2vec(b)) . The angle between vec(a) and vec(b) is :