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 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 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 , 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 vec a , vec b , vec c are unit vectors such that vec a. vec b=0= vec a. vec c and the angle between vec b and vec c is pi/3, then find the value of | vec axx vec b- vec axx vec c| .

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\ represent the sides of a triangle taken in order, then write the value of vec a+ vec b+ vec c

If vec a , vec ba n d vec c are three mutually perpendicular vectors, then the vector which is equally inclined to these vectors is a. vec a+ vec b+ vec c b. vec a/(| vec a|)+ vec b/(| vec b|)+ vec c/(| vec c|) c. vec a/(| vec a|^2)+ vec b/(| vec b|^2)+ vec c/(| vec c|^2) d. | vec a| vec a-| vec b| vec b+| vec c| vec c

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 c are three vectors such that vec a=vec b+vec c and the angle between vec b and vec c is pi/2, then