A force of - P k ^ acts on the origin of the coordinate system. The torque about the point ( 2 , - 3 ) is P ( a i ^ + b j ^ ) , The ratio of a b is x 2 . The value of x is

Step-by-step solution

It is given that the force F → = - P k ^ The coordinates of the origin is ( 0 , 0 ) . The coordinates of the point given is ( 2 , - 3 ) The displacement vector is r → = ( 0 - 2 ) i ^ + ( 0 + 3 ) j ^ = - 2 i ^ + 3 j ^ Hence, the torque is τ → = r → × F → = ( - 2 i ^ + 3 j ^ ) × ( - P k ^ ) ⇒ τ → = - 2 P j ^ - 3 P i ^ = P ( a i ^ + b j ^ ) So, it can be written a = - 3 , b = - 2 ∴    a b = 3 2 ⇒ so x = 3