Linear Vector function of a vector

[Winzer]

Homework Statement

For each state wheather the function is a linear vector function of $$\vec{v}$$

Homework Equations

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

The Attempt at a Solution

I don't get what they mean. The book makes it look ambigious.

 

[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?

 

[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

 

[foxjwill]

great!