A particle travels on a given straight line with a constant speed v . At a certain time, it is at a point P on its straight line path. O is a fixed point. The quantity OP v is

Step-by-step solution

Let the straight line path of the particle be represented by the equation r = r ₀ + v t , where r ₀ is the position vector of a fixed point on the line with respect to the origin O , and v is the constant velocity vector of the particle. The position vector of the particle at any time t is OP = r . The given quantity is OP v . Substituting the expression for OP , we get: OP v = ( r ₀ + v t) v OP v = r ₀ v + t( v v ) Since the cross product of any vector with itself is a null vector ( v v = 0 ), the equation simplif