A particle is displaced from a position `(2 vec i - vec j + vec k)` metre to another position `(3 vec i + 2 vec j -2 vec k)` metre under the action of force `(2 vec i + vec j -vec k)`N. Work done by the force is

Find the value of: (vec j xxvec k) * (3vec i + 2vec j-vec k)

A particle moves with the velocity vec v = (5 vec i + 2 vec j - vec k) ms^(-1) under the influence of a constant force, vec F = (2 vec i + 5 vec j - 10 vec k)N . The instantaneous power applied is

(vec i + xvec j + 3vec k) xx (vec i-vec j + vec k) = 5vec i + xvec j-3vec k then x =

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.

If vec a = i + 2j, vec b = j +2k, vec c = i+2k then vec a . (vec b xx vec c) =

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 distance of the point B with P.V. vec(i) + 2vec(j) + 3vec(k) from the line through A with P.V. 4vec(i) + 2vec(j) + 2vec(k) are parallel to the vector 2vec(i) + 3vec(j) + 6vec(k) is

If vec a=i+j,vec b=j+k and vec c=k+i write unit vectors parallel to vec a+vec b-2vec -

Find the angle between the line vec r=( vec i+2 vec j- vec k)+lambda( vec i- vec j+ vec k) and the normal to the plane vec rdot((2 vec i- vec j+ vec k))=4.

Find the moment of force vec(F) = 4vec(i) + 2vec(j) + vec(k) through the point 5vec(i) + 2vec(j) + 4vec(k) about the point 3vec(i) - vec(j) + 3vec(k) .