The angular velocity of a rotating body is `vec omega = 4 hat i + hat j - 2 hat k`. The linear velocity of the body whose position vector `2hati + 3 hat j - 3 hat k` is

The angular velocity of a body is vec (omega)- = 2 hat(i) + 3 hat(j) + 4 hat (k) and torque hat(tau) = hat(i) + 2 hat(j) + 3 hat(k) acts on it. The rotational power will be

The linear velocity of a rotating body is given by vec(v)= vec(omega)xxvec(r ) , where vec(omega) is the angular velocity and vec(r ) is the radius vector. The angular velocity of a body is vec(omega)= hat(i)-2hat(j)+2hat(k) and the radius vector vec(r )= 4hat(j)-3hat(k) , then |vec(v)| is

Work done by a force F on a body is W = F .s, where s is the displacement of body. Given that under a force F = (2 hat I +3 hat j +4 hat k) N a body is displaced from position vector r_1 = (2 hat I +3 hat j + hat k) m to the position vector r_2 = (hat i +hat j+ hat k) m. Find the work done by this force.

The linear velocity of a rotating body is given by vec(v)=vec(omega)xxvec(r) , where vec(omega) is the angular velocity and vec(r) is the radius vector. The angular velocity of a body is vec(omega)=hat(i)-2hat(j)+2hat(k) and the radius vector vec(r)=4hat(j)-3hat(k) , then |vec(v)| is-

Let vec a= hat i+2 hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec c= hat i+ hat j- hat kdot A vector in the plane of vec a and vec b whose projection of c is 1//sqrt(3) is a. 4 hat i- hat j+4 hat k b. 3 hat i+ hat j+3 hat k c. 2 hat i+ hat j+2 hat k d. 4 hat i+ hat j-4 hat k

Show that the point A , B and C with position vectors vec a =3 hat i - 4 hat j -4 hat k = 2 hat i j + hat k and vec c = hat i - 3 hat j - 5 hat k , respectively from the vertices of a right angled triangle.

Let vec a=2 hat i- hat j+ hat k , vec b= hat i+2 hat j= hat ka n d vec c= hat i+ hat j-2 hat k be three vectors. A vector in the plane of vec ba n d vec c , whose projection on vec a is of magnitude sqrt(2//3) , is a. 2 hat i+3 hat j-3 hat k b. 2 hat i-3 hat j+3 hat k c. -2 hat i- hat j+5 hat k d. 2 hat i+ hat j+5 hat k

The position of a particle is given by vec r = hat i + 2hat j - hat k and its momentum is vec p = 3 hat i + 4 hat j - 2 hat k . The angular momentum is perpendicular to

The position vectors of the points P and Q are 5 hat i+7 hat j- 2 hat k and -3 hat i+3 hat j+6 hat k respecively. The vector vec A=3 hat i-hat j+hat k passes through the point P and the vector vec B=-3 hat i+2 hat j+4 hat k passes through the point Q. A third vector 2 hat i+7 hat j- 5hat k intersects vectors vec A and vec B . Find the position vectors of the points of intersection