If a force `vec(F) = (vec(i) + 2 vec(j)+vec(k)) N` acts on a body produces a displacement of `vec(S) = (4vec(i)+vec(j)+7 vec(k))m`, then the work done is

If vec(a)= 2vec(i)-3 vec(j) + vec(k). vec(b)= vec(i) + 4vec(j)- 2vec(k) , then find (vec(a) + vec(b)) xx (vec(a) - vec(b)) .

Find the torque of the resultant of the three forces represented by -3 vec(i) + 6 vec(j) - 3 vec(k) , 4 vec(i) - 10 vec(j) + 12 vec(k), and 4 vec(i) + 7 vec(j) acting at the point with position vector 8 vec(i) - 6 vec(j) - 4 vec(k) , about the point with position vector 18 vec(i) + 3 vec(j) - 9 vec(k) .

A force vec F = (5 vec i+ 3 vec j+ 2 vec k) N is applied over a particle which displaces it from its origin to the point vec r=(2 vec i- vec j) m . The work done on the particle in joules is.

A force vec F = (5 vec i+ 3 vec j+ 2 vec k) N is applied over a particle which displaces it from its origin to the point vec r=(2 vec i- vec j) m . The work done on the particle in joules is.

A force F = (2 vec i + vec j + vec k)N is acting on a particle moving with constant velocity vec v = (vec i + 2 vec j + vec k)m/s . Power delivered by force is

If vec F =2 hat i + 3hat j +4hat k acts on a body and displaces it by vec S =3 hat i + 2hat j + 5 hat k , then the work done by the force is

Assertion (A): The torque about the point 3vec(i)-vec(j) + 3vec(k) of a force represented by 4vec(i) + 2vec(j) + vec(k) through the point 5vec(i) + 2vec(j) + 4vec(k) is vec(i) + 2vec(j)-8vec(k) Reason (R ): The torque of a force F about a point P is vec(r ) xx vec(F ) where vec(r ) is the vector from the point P to any point vec(a) on the line of action of vec(F ) Which of the following is correct ?

If vec(a)= 2vec(i) + 5vec(j) + vec(k) and vec(b)=4vec(i) + mvec(j) + n vec(k) are collinear vectors, then find the m and n

vec(a)= 3vec(i)- vec(j) + 2vec(k), vec(b)= -vec(i) + 3vec(j) + 2vec(k), vec(c )= 4vec(i) + 5vec(j)- 2vec(k) and vec(d)= vec(i) + 3vec(j) + 5vec(k) , then compute (vec(a) xx vec(b)).vec( c) - (vec(a) xx vec(d)).vec(b)

If vec(a)= vec(i) + vec(j) + vec(k), vec(b)= -vec(i) + 2vec(j) + vec(k), vec(c )= vec(i) + 2vec(j) -vec(k) then a unit vector perpendicular to vec(a) + vec(b) and vec(b) + vec(c ) is