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 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 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 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 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 axx vec b= vec cxx vec da n d vec axx vec c= vec bxx vec d , then show that vec a- vec d , is paralelto vec b- vec c

If vec axx vec b= vec axx vec c , vec a!= vec0a n d vec b!= vec c , show that vec b= vec c+t vec a for some scalar tdot

If veca , vec b and vec c represents three sides of a triangle taken in order prove that veca xx vec b = vec b xx vec c = vec c xx vec a

Prove that the points A ,Ba n d C with position vectors vec a , vec ba n d vec c respectively are collinear if and only if vec axx vec b+ vec bxx vec c+ vec cxx vec a= vec0dot

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 veca , vec b , vec c are three vectors such that veca+ vec b+ vec c= vec0 , then prove that vec axx vec b= vec bxx vec c= vec cxx vec a