Vector Calculus (Position Vector)

The position vector of a point is given by . Prove that:

a)

b) the angle between the position vector and the acceleration vector is constant. Calculate this angle.

Answer: b) pi/2

____________________________________________

I tried to derive the position vector two times but it isn't working.

Re: Vector Calculus (Position Vector)

Quote:

Originally Posted by

**PedroMinsk** The position vector of a point is given by

. Prove that:

a)

b) the angle between the position vector

and the acceleration vector

is constant. Calculate this angle.

This is a tedious problem.

Luckily there are web resources

BE SURE to click "show steps"

You can change the question to .

That will help you find the second derivative or

Re: Vector Calculus (Position Vector)

For the second question you can calculate the scalar product of the vectors like:

The scalar produt will tell you more about the angle between the vectors, but first you've to determine the coordinates of the vector r(t) (see Plato's post).

Re: Vector Calculus (Position Vector)

Thanks. I got the idea. I only knew the Wolfram integrator, this one will help me a lot.

Can I calculate the angle using dot product? Or there is another way?

Re: Vector Calculus (Position Vector)

The dot (or scalar) product is very useful here, you'll come to the conclusion if you calculate the dot product that it will be 0 and ( )

Re: Vector Calculus (Position Vector)

Quote:

Originally Posted by

**PedroMinsk** Thanks. I got the idea. I only knew the Wolfram integrator, this one will help me a lot.

Can I calculate the angle using dot product? Or there is another way?

Yes the dot product, see reply #3.

You should explore what all **wolframalpha** will do.

Look at this.

Re: Vector Calculus (Position Vector)

I got it. Thanks. I will see the link.