If the position vectors of the points A,B and C be a,b and 3a-2b respectively, then prove that the points A,B and C are collinear.

If the position vectors of the points A,B and C be hati+hatj,hati-hatj and ahati+bhatj+chatk respectively, then the points A,B and C are collinear, if

If the position vectors of the points A and B are 3i+j+2k and i-2 j-4k respectively, then the equation of the plane through B and perpendicular to AB is

If the position vectors of the points A and B respectively are i+2j-3k and j-k find the direction cosines of AB

If veca and vecb are position vectors of the points A and B respectively, then position vector of a point C in AB produced such that AC = 3AB is :

Show that the points A(1,3,2),B(-2,0,1) and C(4,6,3) are collinear.

The position vectors of the points A and B are veca and vecb respectively. P divided [AB] in the ratio 3:1, Q is mid-point of [AP]. The positin vector of Q is :

Show that the points A(1,2,7),B(2,6,3) and C(3,10,-10 are collinear.

If the position vectors of the points A and B are hati+3hatj-hatk and 3hati-hatj-3hatk , then what will be the position vector of the mid-point of AB

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 a and b are position vector of two points A,B and C divides AB in ratio 2:1, then position vector of C is