If `2vec(AC)=3vec(CB)`, then prove that `2vec(OA)+3vec(OB)=5vec(OC)` where `O` is the origin.

If 2 vec A C = 3 vec C B , then prove that 2 vec O A =3 vec C B then prove that 2 vec O A + 3 vec O B =5 vec O C where O is the origin.

ABCD is a quadrilateral and E is the point of intersection of the lines joining the middle points of opposite side. Show that the resultant of vec (OA) , vec(OB) , vec(OC) and vec(OD) = 4 vec(OE) , where O is any point.

Assertion: If I is the incentre of /_\ABC, then |vec(BC)| vec(IA) +|vec(CA)| vec(IB) +|vec(AB)| vec(IC) =0 Reason: If O is the origin, then the position vector of centroid of /_\ABC is (vec(OA)+vec(OB)+vec(OC))/3

If 2veca, 3vecb,2(veca xx vecb) are position vectors of the vectors A,B,C, of triangleABC and |veca|=|vecb|=1,vec(OA).vec(OB)=-3 (where O is the origin), then

Let A and B be points with position vectors veca and vecb with respect to origin O . If the point C on OA is such that 2vec(AC)=vec(CO), vec(CD) is parallel to vec(OB) and |vec(CD)|=3|vec(OB)| then vec(AD) is (A) vecb-veca/9 (B) 3vecb-veca/3 (C) vecb-veca/3 (D) vecb+veca/3

If two points A and B lie on the curve y=x^(2) such that vec(OA).hati=1 and vec(OB).hatj=4 , where O is origin and A and B lie in the 1^("st") and 2^("nd") quadrant respectively, then vec(OA).vec(OB) is equal to

If O is the circumcentre and P the orthocentre of Delta ABC , prove that vec(OA)+ vec(OB) + vec(OC) =vec(OP) .

Let O be an interior point of triangle ABC, such that 2vec(OA)+3vec(OB)+4vec(OC)=0 , then the ratio of the area of DeltaABC to the area of DeltaAOC is

If |vec (AO) +vec (OB)| =|vec(BO) + vec(OC)| , then A, B, C form

Find the resultant of the three vectors vec(OA), vec(OB) and vec(OC) shown in figure. Radius of the circle is R.