The position vectors of four points P,Q,R annd S are `2a+4c`,5a+`3sqrt(3)b+4c,-2sqrt(3)b+c and 2a+c` respectively, prove that PQ is parallel to RS.

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.

The position vectors of the points A,B and C are hati+2hatj-hatk,hati+hatj+hatk and 2hati+3hatj+2hatk , respectively. If A is chosen as the origin, then the position vectors of B and C are

The position vectors of the points A, B, C are 2 hati + hatj - hatk , 3 hati - 2 hatj + hatk and hati + 4hatj - 3 hatk respectively . These points

Statement 1: Let vec a , vec b , vec ca n d 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 three points A,B and C have position vectors (1,x,3),(3,4,7) and (y,-2,-5), respectively and if they are collinear, then find x,y.

The sum and product of the zeroes an a quadratic polynomial P (x) = ax^(2) + bx +c are -3 and 2 respectively, Show that b+c = 5a.

Show that the points A,B and C having position vectors (3hati - 4hatj - 4hatk), (2hati - hatj + hatk) and (hati - 3hatj - 5hatk) respectively, from the vertices of a right-angled triangle.

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

If the position vectors of P and Q are (hati+3hatj-7hatk) and (5hati-2hatj+4hatk) , then |PQ| is

The position vector of a point C with respect to B is hat i +hat j and that of B with respect to A is hati-hatj . The position vector of C with respect to A is