The position vectors of two point masses 10 kg and 5 kg are `(-3vec(i)+2vec(j)+4vec(k))m " and " (3vec(i)+6vec(j)+5vec(k))m` respectively. Locate the position of centre of mass.

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.

Find the angle between the vectors vec(i) + 2vec(j) + 3vec(k) and 3vec(i) - vec(j) + 2vec(k) .

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

The position vectors of the vertices of a triangle are vec(i) +2 vec(j) +3 vec(k) , 3 vec(i) -4 vec(j) +5 vec (k) and -2vec (i) +3 vec (j) - 7 vec (k) Find the perimeter of a triangle .

The vector area of the parallelogram whose diagonals are vec(i) + 2vec(j) + 3vec(k), -vec(i) - 2vec(j) + vec(k) is

Find the unit vectors perpendicular to both the vectors 2vec(i)- 3vec(j) + 5vec(k) and -vec(i) + 4vec(j) + 2vec(k)

(2 vec(i) + 4vec(j) + 2vec(k)) xx (2vec(i) -p vec(j) + 5vec(k))=16 vec(i) -6vec(j) + 2p vec(k) then p=

If the vectors 2vec(i)-qvec(j)+3vec(k) and 4vec(i)-5vec(j)+6vec(k) are collinear, the value of q is

A unit vector perpendicular to 2vec(i) + 3vec(j) + 4vec(k) and 3vec(j) + 2vec(k) is

A vector of magnitude 6 which is perpendicular to both 4vec(i) - vec(j) + 3vec(k) and -2vec(i) + vec(j) - 2vec(k) is