Why is a·(b×c) = b·(c×a) = c·(a×b)?

[phospho]

Im having trouble understanding this property

my book states that: a.(bxc) = b.(cxa) = c.(axb)

it also states that a.(ax(anything)) = 0

I understand the second point and why that's true, what I don't understand is why a.(bxc) = b.(cxa) = c.(axb) is true

If I name any 3 vectors a b and c would this be true? I'm just really confused to why it works, and my book doesn't really go into depth as it's a high school book, and Wikipedia seems to be vague or too complex for me.

 

[LCKurtz]

Im having trouble understanding this property

my book states that: a.(bxc) = b.(cxa) = c.(axb)

it also states that a.(ax(anything)) = 0

I understand the second point and why that's true, what I don't understand is why a.(bxc) = b.(cxa) = c.(axb) is true

If I name any 3 vectors a b and c would this be true? I'm just really confused to why it works, and my book doesn't really go into depth as it's a high school book, and Wikipedia seems to be vague or too complex for me.

Do you have the property that you can interchange the dot and cross? If not, you should show that first. Then try it on a.(bxc) and see if you can get one of the other forms remembering that the dot product is commutative.

 

[phospho]

Do you have the property that you can interchange the dot and cross? If not, you should show that first. Then try it on a.(bxc) and see if you can get one of the other forms remembering that the dot product is commutative.

no, I don't - what is this property?

 

[LCKurtz]

Do you have the property that you can interchange the dot and cross? If not, you should show that first. Then try it on a.(bxc) and see if you can get one of the other forms remembering that the dot product is commutative.

no, I don't - what is this property?

a.(bxc) = (axb).c