Applying the Product Rule to Vector Dot Products

[MeMoses]

Homework Statement

I have vector R. I need to show the R dot dR/dt = 0 => 1/2 d/dt[R dot R]

Homework Equations

The Attempt at a Solution

I guess I've never really applied the chain rule to dot products and its throwing me off. How does one go from R.dR/dt=0 to 1/2 d/dt[R.R] = 0. I have no idea to be honest. I'm not sure which direction to take it, all I know is it uses the chain rule. Sorry I haven't done much with this. I hope you can help. Thanks

 

[Curious3141]

Homework Statement

I have vector R. I need to show the R dot dR/dt = 0 => 1/2 d/dt[R dot R]

Homework Equations

The Attempt at a Solution

I guess I've never really applied the chain rule to dot products and its throwing me off. How does one go from R.dR/dt=0 to 1/2 d/dt[R.R] = 0. I have no idea to be honest. I'm not sure which direction to take it, all I know is it uses the chain rule. Sorry I haven't done much with this. I hope you can help. Thanks

Actually it uses the product rule, which applies to vector dot products too. See: http://en.wikipedia.org/wiki/Product_rule#For_vector_functions

Try applying that on the second part, i.e. what is d/dt (R.R)?