1. ## Simplifying Cross Products

Hi guys

I'm boggled by this problem

a x (b x (a x b))

I know the first step is to simplify the triple vector product inside the () which leads this expression

a x (( b dot b)a - (b dot a)b)

but the book claims that the final answer is eventually

(- a dot ba x b)

Can someone explain why?

2. Originally Posted by gotpho
Hi guys

I'm boggled by this problem

a x (b x (a x b))

I know the first step is to simplify the triple vector product inside the () which leads this expression

a x (( b dot b)a - (b dot a)b)

but the book claims that the final answer is eventually

(- a dot ba x b)

Can someone explain why?

$
b \cdot b \left( a \times a\right) - a \cdot b \left( a \times b\right)
$

noting that $a \times a = 0$.

3. Never knew you could distribute like that

But isn't a dot a = |a|^2. How do you know that they are orthogonal?

4. Originally Posted by gotpho
Never knew you could distribute like that

But isn't a dot a = |a|^2. How do you know that they are orthogonal?
I believe it's $a \times a$ not $a \cdot a.$

5. Originally Posted by Danny
I believe it's $a \times a$ not $a \cdot a.$