Question about the Triple Product

[influx]

Homework Statement

[/B]

Homework Equations

a⋅(b x a) = 0

The Attempt at a Solution

Is my working below correct? In particular, can you apply the r_CB to both the first part of the bracket (0.2j) and the second part (w x r_CB) individually like that?

My second question relates to:

Is that correct? Does it matter if r_CB is multiplied at the end or start? I am inclined to think it doesn't as it's a dot product?

 

[fresh_42]

Both are correct. The first because the dot product is (bi-)linear, the second, because it is symmetric.
For the third term to equal zero, you can use the identity $(\vec{a}\times \vec{b}) \cdot \vec{c} = (\vec{b}\times \vec{c}) \cdot \vec{a} = (\vec{c}\times \vec{a}) \cdot \vec{b}$ and the anti-symmetry of the cross product: $\vec{a}\times \vec{a} = \vec{0}$.