If ` vec A O+ vec O B= vec B O+ vec O C` , then `A ,Bn a dC` are (where `O` is the origin) a. coplanar b. collinear c. non-collinear d. none of these

If vec a ,\ vec b ,\ vec c are three non-zero vectors, no two f thich are collinear and the vector vec a+ vec b is collinear with vec c ,\ vec b+ vec c is collinear with vec a ,\ t h e n\ vec a+ vec b+ vec c= a. vec a b. vec b c. vec c d. none of these

(vec a xxvec b)xx(vec b xxvec c)=vec b, where vec a,vec b, and vec c are nonzero vectors,then vec a,vec b, and vec c can be coplanar vec a,vec b, and vec c must be coplanar vec a,vec b, and vec c cannot be coplanar none of these

36. If vec a, vec b, vec c and vec d are unit vectors such that (vec a xx vec b) .vec c xx vec d = 1 and vec a.vec c = 1/2 then a) vec a, vec b and vec c are non-coplanar b) vec b, vec c, vec d are non -coplanar c) vec b, vecd are non parallel d) vec a, vec d are parallel and vec b, vec c are parallel

If vec a , vec b , vec c , vec d are the position vector of point A , B , C and D , respectively referred to the same origin O such that no three of these point are collinear and vec a + vec c = vec b + vec d , than prove that quadrilateral A B C D is a parallelogram.

If vec rdot vec a= vec rdot vec b= vec rdot vec c=1/2 or some nonzero vector vec r , then the area of the triangle whose vertices are A( vec a),B( vec b)a n dC( vec c)i s( vec a , vec b , vec c are non-coplanar) |[ vec a vec b vec c]| b. | vec r| c. |[ vec a vec b vec c] vec r| d. none of these

vec axx( vec bxx vec c) , vec bxx( vec cxx vec a) and vec cxx( vec axx vec b) are: linearly dependent (b) coplanar vector parallel vectors (d) non coplanar vectors

If vec a,vec b and vec c are three non-zero vectors,no two of which ar collinear,vec a+2vec b is collinear with vec c and vec b+3vec c is collinear with vec a then find the value of |vec a+2vec b+6vec c|

If O A B C is a tetrahedron where O is the orogin anf A ,B ,a n dC are the other three vertices with position vectors, vec a , vec b ,a n d vec c respectively, then prove that the centre of the sphere circumscribing the tetrahedron is given by position vector (a^2( vec bxx vec c)+b^2( vec cxx vec a)+c^2( vec axx vec b))/(2[ vec a vec b vec c]) .

If vec a + vec b + vec c = o, prove that vec a xxvec b = vec b xxvec c = vec c xxvec a

Given four vectors vec a, vec b, vec c, vec d such that vec a + vec b + vec c = alphavec d, vec b + vec c + vec d = betavec a and that vec a, vec a, vec b, vec c are non-coplanar, then the sum vec a + vec b + vec c + vec d is