If ` vec a ,\ vec b ,\ vec c` are position vectors of the vertices of a triangle, then write the position vector of its centroid.

If vec a ,\ vec b ,\ vec c are the position vectors of the vertices of an equilateral triangle whose orthocentre is the origin, then write the value of vec a+ vec b+ vec c

If veca , vec b , vec c are the position vectors of the vertices A ,B ,C of a triangle A B C , show that the area triangle A B Ci s1/2| vec axx vec b+ vec bxx vec c+ vec cxx vec a|dot Deduce the condition for points veca , vec b , vec c to be collinear.

If vec a ,\ vec b ,\ vec c are position vectors of the vertices A ,\ B\ a n d\ C respectively, of a triangle A B C ,\ write the value of vec A B+ vec B C+ vec C Adot

If vec a and vec b are position vectors of points Aa n dB respectively, then find the position vector of points of trisection of A B .

If vec(a), vec(b), vec(c) are the position vectors of vertices A, B, C of a triangle ABC, Show that the area of the triangle is (1)/(2) |vec(b) xx vec(c) + vec(c) xx vec(a) + vec(a) xx vec(b)|

If vec a ,\ vec b ,\ vec c are position vectors o the point A ,\ B ,\ a n d\ C respectively, write the value of vec A B+ vec B C+ vec A Cdot

If vec a ,\ vec b ,\ vec c be the vectors represented by the sides of a triangle, taken in order, then prove that vec a+ vec b+ vec c= vec0dot

If vec a , vec b , vec ca n d vec d are the position vectors of the vertices of a cyclic quadrilateral A B C D , prove that (| vec axx vec b+ vec bxx vec d+ vec d xx vec a|)/(( vec b- vec a)dot( vec d- vec a))+(| vec bxx vec c+ vec cxx vec d+ vec d xx vec b|)/(( vec b- vec c)dot( vec d- vec c))=0dot

If veca and vecb are position vectors of A and B respectively, then the position vector of a point C in vec(AB) produced such that vec(AC) =2015 vec(AB) is

Let ABCD be as parallelogram. If vec a ,\ vec b ,\ vec c be the position vectors of\ A ,\ B ,\ C respectively with reference to the origin O, find the position vector of D reference to O.