A particle which is experiencing a force, given by `vec(F) = 3 vec(i) - 12 vec(j)`, undergoes a displacement of `vec(d) = 4 vec(i)`. If the particle had a kinetic energy of 3 J at the beginning of the displacement

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

During a storm, a crate of crepe is sliding across a slick, oily parking lot through a displacement vec(d)=(-3.0m)hat(i) while a steady wind pushes against the crate with a force vec(F)=(2.0N)hat(i)+(-6.0N)hat(j) . The situation and coordinate axes are shown in Fig. 8-6. If the crate has a kinetic energy of 10 J at the beginning of displacement vec(d) , what is its kinetic energy energy at the end of vec(d) ?

If vec(a)= 2vec(i) -vec(j) + 3vec(k), vec(b)= p vec(i) + vec(j) + q vec(k) and vec(b) xx vec(a) = vec(0) , then

A particle has initial velocity vec(v)=3hat(i)+4hat(j) and a constant force vec(F)=4hat(i)-3hat(j) acts on the particle. The path of the particle is :

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

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

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) .

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 position of the particle is given by vec(r )=(vec(i)+2vec(j)-vec(k)) momentum vec(P)= (3vec(i)+4vec(j)-2vec(k)) . The angular momentum is perpendicular to

Examine if vec(i) - 3vec(j) + 2vec(k), 2vec(i) - 4vec(j) - vec(k) and 3vec(i) + 2vec(j) - vec(k) are linearly independent or dependent .