How to identify that a vector is directed away from the origin or towards the originFor example in the following question it`s clear that the answer is perpendicular but how to identify if neededQuestion= the position vector of a particle is Vector(r)=(acoswt) i +(asinwt) jThe velocity of the particle isOption A directed towards the originOption B directed away from the originOptions c parallel to the position vectorOption d perpendicular to the position vector

Dear student,

Finding if a random vector is directed towards or away from origin is tough by looking at the time dependent variation of it since it not only depends upon its direction but also its point of origin. You could take scalar product of the position vecotor of the point of origin of the given vector and the vector itself. If the product is positive, it is directed awayf from origin. If negative, it is directed towards it. If it comes out to be zero, it is perpendicular to the position vector.

However, it is suggested to try to picture it graphically instead. For example, in the above question , the position vector travels in a circle centered at origin. Hence the velocity vecotor will be along the tangent of the cirlce, and hence always pernpendicular to the position vector.