Let `vec a` and `vec b` be the position vectors of the points (3,-5) and (m,4) respectively. Find m if the vectors `vec a` and `vec b` are collinear.

If vec a , vec b are the position vectors of the points (1,-1),(-2,m), find the value of m for which vec aa n d vec b are collinear.

If vec a and vec b are the position vectors of A and B respectively, find the position vector of a Point C in BA produced such that BC = 1.5 BA.

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.

The position vector of the point which divides the join of points with position vectors vec a+vec b and 2vec a-vec b inthe ratio 1: 2 is

The position vector of the point which divides the join of points 2 vec a -3 vec b and vec a+vec b in the ratio 3: 1 is

Statement 1: Let vec a , vec b , vec c and vec d be the position vectors of four points A ,B ,Ca n dD and 3 vec a-2 vec b+5 vec c-6 vec d=0. Then points A ,B ,C ,a n dD are coplanar. Statement 2: Three non-zero, linearly dependent coinitial vector ( vec P Q , vec P Ra n d vec P S) are coplanar. Then vec P Q=lambda vec P R+mu vec P S ,w h e r elambdaa n dmu are scalars.

If vec a and vec b are two collinear vectors then which of the following are incorrect :

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