# Linear Vector function of a vector

1. Jun 18, 2008

### Winzer

1. The problem statement, all variables and given/known data
For each state wheather the function is a linear vector function of $$\vec{v}$$

2. Relevant equations
1.$$\vec{F}(\vec{v})=\alpha \vec{v}$$
2. $$\vec{F}(\vec{v})= \vec{a} \times (\vec{b} \times \vec{v}) + (\vec{a} \times \vec{v}) \times \vec{v}$$

3. The attempt at a solution
I don't get what they mean. The book makes it look ambigious.

2. Jun 18, 2008

### foxjwill

They make what look ambiguous? The definition of a linear function? A linear function is a function f such that

$$f(\vec{x}+\vec{y})=f(\vec{x})+f(\vec{y})$$
$$f(a\vec{x})=af(\vec{x}).$$​

Edit: Or, are you not sure what they mean by F being a function of v?

B.T.W., do you know the formula for the vector triple product?

3. Jun 18, 2008

### Winzer

Actually I get it, it was presented differently in the book. It's all so trivial now. And yes I do know the formula for a triple product

4. Jun 18, 2008

great!