quick maths vector question?

Question

what does r = a + t(b-a) represent???

Answer 1

point A has position vector a
point B has position vector b
b - a is vector AB
r is position vector of a point on vector AB
r = a + t AB
r = a + t (b - a)

Answer 2

r = a + t(b-a)
r, the radial vector is probably the displacement cordiante as a function of time. It is a linear function of t. If the angle theta is independent of time (since it is not given here), we can assume the particle to be progressing 1-D along a stright line with constant velocity (b-a)