Suppose r(t) = (et cos t)i + (et sin t)j. Show that the angle between r and a never changes. What is the angle?

Angle = Ф = (0) = 0

Hence, it is proved that angle between position vector r and acceleration vector a = 0 and is it never changes.

Step-by-step explanation:

Given vector r(t) =

As we know that,

velocity vector = v =

Implies that

velocity vector =

As acceleration is velocity over time so:

acceleration vector = a =

Implies that

vector a =

vector a =

Now scalar product of position vector r and acceleration vector a:

r. a =

r.a =

r.a = 0

Now, for angle between position vector r and acceleration vector a is given by:

cosФ = =

Ф = (0) = 0

Hence, it is proved that angle between position vector r and acceleration vector a = 0 and is it never changes.