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 the vertices A,B,C of a triangle ABC, show that the area triangle ABCis(1)/(2)|vec a xxvec b+vec b xxvec c+vec c xxvec a| Deduce the condition for points vec a,vec b,vec c to be collinear.

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

If vec a , vec b , vec c and vec d are the position vectors of points A, B, C, D such that no three of them are collinear and vec a + vec c = vec b + vec d , then ABCD is a

If vec(a), vec(b), vec(c ) are the position vectors of the vecrtices A, B, C of a Delta ABC respectively, find an expression for the area of Delta ABC and hence deduce the condition for the points A, B, C to be collinear.

[vec a+vec b,vec b+vec c,vec c+vec a]=2[vec a,vec b,vec c]

If vec a,vec b and vec c are the position vectors of the vertices A,B and C respect ively,of bigoplus ABC , prove that the perpendicular distance of the vertedx A from the base BC of the triangle ABC is (|vec a xxvec b+vec b xxvec c+vec c xxvec a|)/(|vec c-vec b|)

[[vec a + vec b-vec c, vec b + vec c-vec a, vec c + vec a-vec b is equal to

[vec a + vec b, vec b + vec c, vec c + vec a] = 2 [vec a, vec b, vec c]

If vec a,vec b,vec c are the position vectors of points A,B,C and D respectively such that (vec a-vec d)*(vec b-vec c)=(vec b-vec d)*(vec c-vec a)=0 then D is the

If the vectors vec a , vec b ,a n d vec c form the sides B C ,C Aa n dA B , respectively, of triangle A B C ,t h e n vec adot vec b+ vec bdot vec c+ vec cdot vec a=0 b. vec axx vec b= vec bxx vec c= vec cxx vec a c. vec adot vec b= vec bdot vec c= vec cdot vec a d. vec axx vec b+ vec bxx vec c+ vec cxx vec a=0