Are Orthogonal Vectors Proven by Derivative and Dot Product?

[guyvsdcsniper]

Homework Statement

Prove that if v(t) is any vector that depends on time, but v(t) has constant magnitude, then
v˙(t) is orthogonal to v(t)

Relevant Equations

Dot Product

I feel like this question is very straight forward and my explanation below summarizes the answer pretty well. Could someone confirm this or tell me if I am missing something?

We have V which is a vector, but the question states it is a constant. If I take the derivative of V, represented by V', a constant, then I get 0.
If I dot product these to values, the product is then 0. And it is known that when the dot product between two vectors is zero, they are orthogonal.

 

[PeroK]

Homework Statement:: Prove that if v(t) is any vector that depends on time, but v(t) has constant magnitude, then
v˙(t) is orthogonal to v(t)
Relevant Equations:: Dot Product

I feel like this question is very straight forward and my explanation below summarizes the answer pretty well. Could someone confirm this or tell me if I am missing something?

We have V which is a vector, but the question states it is a constant. If I take the derivative of V, represented by V', a constant, then I get 0.
If I dot product these to values, the product is then 0. And it is known that when the dot product between two vectors is zero, they are orthogonal.

It says that $\vec v$ has constant magnitude; not that $\vec v$ is constant.

 

[guyvsdcsniper]

It says that $\vec v$ has constant magnitude; not that $\vec v$ is constant.

Ah I misread the question. That makes a lot of sense. Thank you for catching that.

 

[BvU]

So what does it look like now?

 

[guyvsdcsniper]

So what does it look like now?

This is the conclusion I came to.