If the position vectors of the points `A(3,4),B(5,-6)` and `(4,-1)` are ` vec a , vec b , vec c` respectively compute ` vec a+2 vec b-3 vec cdot`

If vec a,vec b and vec c are the position vectors of the points A(2,3,-4),B(3,-4,-5) and C(3,2,-3) respectively,then |vec a+vec b+vec c| is equal to

The position vectors of the points A,B,C are vec a, vec b, vec c respectively. If 3 vec a + 2 vec c= 5 vecb , are the points A,B,and C collinear? If so find AB:BC .

The position vectors of A,B,C and D are vec a,vec b,vec 2a+vec 3b and vec a-vec 2b respectively show that vec DB=3vec b-vec a and vec AC=vec a+vec 3b

If vec (a),vec (b) and vec (c) are the position vectors of the points A(2,3,-4), B(3,-4,-5) and C(3,2,-3) respectively ,then |vec(a)+vec(b)+vec(c)| is equal to (A) sqrt(113) (B) sqrt(185) (C) sqrt(203) (D) sqrt(209)

If the position vectors of three points are vec a-2vec b+3vec c,2vec a+3vec b-4vec c,-7vec b+10vec c then the three points are

The position vectors of three points are 2vec a-vec b+3vec c,vec a-2vec b+xvec c and yvec a-5vec b where vec a,vec b,vec c are non coplanar vectors.If the three points are collinear then

vec a,vec b and vec c are the position vectors of points A,B and C respectively,prove that: vec a_(vec a)xvec b+vec bxvec c+vec cxvec a is vector perpendicular to the plane of triangle ABC.

If vec(b) and vec(c) are the position vectors of the points B and C respectively, then the position vector of the point D such that vec(BD) = 4 vec(BC) is

If vec(b) and vec(c ) are the position vectors of the points B and C respectively, then the position vector of the point D such that vec(BD)= 4 vec(BC) is

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