The position vector of the points A, B and C are respectively `vec i + vec j, vec j + vec k` and `lambda vec k + vec i`. If the volume of the tetrahedron OABC is 6, find `lambda` where O is the origin.

The position vectors of three A,B, and C in space are respectively 2 vec i + 3 vec j - vec k, vec i - 2 vec j + 3 vec k and 4 vec i + vec j + vec k . Find the volume of the parallelepiped whose three concurrent edges are OA, OB and OC where O is the origin.

The position vectors of the points A and B are vec i + 2 vec j + 3 vec k and 2 vec i - vec j - vec k respectively. Find the projection of vec (AB) on the vector vec i + vec j + vec k . Also find the resolved part of vec (AB) in that direction.

The position vectors of the points A,B,C , D are respectively 2 vec i + vec j - vec k, vec i + vec j + vec k, vec i- 2 vec j+ 3 vec k and 3 vec i- vec j + 2 vec k . Evaluate [vec (AB), vec (AC), vec (AD)] .

The position vectors of three points are -2vec i+3vec j+5vec k,vec i+2vec j+3vec k,7vec i-vec k Show that the three points are collinear

Find the unit vector in the direction of the vector vec a + vec b if vec a =vec i +2 vec j + 3 vec k and vec b = 2 vec i + 3 vec j + 5 vec k .

The position vectors of three points are vec i+3vec j-2vec k,3vec i-2vec j+vec k and -2vec i+vec j+3vec k show that the points are the vertices of an equilateral triangle

vec i + vec j + vec k, 4vec i + vec j + vec k, vec 4 + 5vec j + k Then the position vector of the circumcentre of the Delta ABC is

If the position vectors of three consecutive vertices of any parallelogram are respectively vec i+vec j+vec k+vec i+3vec j+5vec k,7vec i+9vec j+11vec k then the position vector of its fourth vertex is:

The position vector of a midpoint lying on the line joining the points whose position vectors are vec i+vec j-vec k and vec i-vec j+vec k is

If the position vectors of two given points A and B be 8vec i+3vec j+2vec k and 2vec i-5vec j+3vec k respectively,find the magnitude and direction of vec AB