The vertices `A , B , C` of triangle `A B C` have respectively position vectors ` vec a , vec b , vec c` with respect to a given origin `O` . Show that the point `D` where the bisector of `/_A` meets `B C` has position vector ` vec d=(beta vec b+gamma vec c)/(beta+gamma),` where `beta=| vec c- vec a|` and, `gamma=| vec a- vec b|dot`

The position vector of A,B are vec a and vec b respectively.The position vector of C is (5(vec a)/(3))-vec b then

If A, B, C are vertices of a triangle whose position vectors are vec a, vec b and vec c respectively and G is the centroid of Delta ABC, " then " vec(GA) + vec(GB) + vec(GC), is

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]) .

Show that the vectors vec a,vec b and vec c are coplanar if vec a+vec b,vec b+vec c and vec c+vec a are coplanar.

Show that the vectors vec a,vec b and vec c are coplanar if vec a+vec b,vec b+vec c and vec c+vec a are coplanar.

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 the vertices A ,Ba n dC of a triangle are three unit vectors vec a , vec b ,a n d vec c , respectively. A vector vec d is such that vecd dot vec a= vecd dot vec b= vec d dot vec ca n d vec d=lambda( vec b+ vec c)dot Then triangle A B C is a. acute angled b. obtuse angled c. right angled d. none of these

Prove that the points A,B and C with position vectors vec a,vec b and vec c respectively are collinear if and only if vec a xxvec b+vec b xxvec c+vec c xxvec a=vec 0

Show that the point A,B,C with position vectors vec a-2vec b+3vec c,2vec a+3vec b-4vec c and -7vec b+10vec c are collinear.

Show that the points with position vectors vec a-2vec b+3vec c,-2vec a+3vec b-vec c and 4vec a-7vec b+7vec c are collinear.