A rigid body is rotating about an axis through the point (3,-1,-2). If the particle at the point (4,1,0) has velocity `4veci-4vecj+2veck` , find the magnitude and direction of the angular velocity of the body.

A rigid body is rotating at 5 radians per second about an axis AB where A and B are the pont 2veci+vecj+veck and 8veci-2vecj+3veck respectively. Find the veclocity of the parcticle P of the body at the points 5veci-vecj+veck .

Find the equation of the plane passes through the point (2,3,-4) and (1,-1,3) and parallel to x-axis.

Find the equation of a line passes through the point (2,3,4) and whose direction ratios are 3,-1,-2 .

A rigid body is spinning about a fixed point (3,-2,-1) with an angular velocity of 4 rad/s, the axis of rotation being in the direction of (1,2,-2). Find the velocity of the particle at point (4,1,1).

A rigid body is spinning about a fixed point (3,-2,-1) with an angular velocity of 4 rad/s, the axis of rotation being in the direction of (1,2,-2). Find the velocity of the particle at point (4,1,1).

A rigid body is free to rotate about an axis. Can the body have non-zero angulalr acceleration of an instant when its angular velocity is zero?

A rigid body rotates about an axis through the origin with an angular velocity 10sqrt(3) rad/s. If omega points in the direction of hat(i)+hat(j)+hat(k) , then the equation to the locus of the points having tangential speed 20m/s.

Find the equation of the plane passing through the point (2, -3, 1) and perpendicular to the line joining points (4, 5, 0) and (1, -2, 4).

Find the equation of the plane through the point 2veci+3vecj-veck and perpendicular to the vector 3veci-4vecj+7veck .

Find the equation of the plane through the point 2veci-vecj+veck and perpendiulr to the vector 4veci+2vecj-3veck . Determine the perpendicular distance of this plane from the origin.