If position vector r = bt^2i + ct^3j, where b and c are positive constants, when does the velocity vector make an angle of 450 with the x-and y-axes?

The velocity at time is

Take two vectors that point in the positive and positive directions, such as and . The dot products of the velocity vector with and are

and

We want the angles between these vectors to be 45º, for which we have . So

When , the velocity vector is equal to the zero vector, which technically has no direction/doesn't make an angle with any other vector. So the only time this happens is for

568.98

explanation:

its math