The angle between and  is θ. The value of the triple product .( × ) is

A bullet is fired from a gun with a speed of 100 m/s in order to hit a target 100m away. At what height above the target should the gun be aimed? (The resistance of air is negligible and g = 10 m/s²)

and  are two vectors and θ is the angle between them, if | × | = √3 ( . ) the value of θ is

A particle starting from the origin (0, 0) moves in a straight line in the (x, y) plane. Its coordinates at a later time are (√3, 3). The path of the particle makes with the x-axis an angle of

A stone is attached to one end of a string and rotated in a vertical circle. If string breaks at the position of maximum tension, it will break at

What is the linear velocity if angular velocity vector and position vector ?

A particle moves along a circle of radius with constant tangential acceleration. If the velocity of the particle is 80 m/s at the end of the second revolution after motion has begun, the tangential acceleration is

A particle of mass m is projected with velocity v making an angle of 45° with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be

If a vector is perpendicular to the vector , then the value of α is

A person swims in a river aiming to reach exactly opposite point on the bank of a river. His speed of swimming is 0.5 m/s at an angle 120° with the direction of flow of water. The speed of water in stream is