## Vector algebra

Analytic Geometry
Tolaso J Kos
Posts: 867
Joined: Sat Nov 07, 2015 6:12 pm
Location: Larisa
Contact:

### Vector algebra

Let $\mathbf{a} , \mathbf{b}, \mathbf{c}$ be three non coplanar vector. If $\displaystyle{\mathbf{a}' = \frac{\mathbf{b} \times \mathbf{c}}{\left [ \mathbf{a,b, c} \right ]} \; , \; \mathbf{b}' = \frac{\mathbf{c} \times \mathbf{a}}{\left [ \mathbf{a,b, c} \right ]} \; , \; \mathbf{c}' = \frac{\mathbf{a} \times \mathbf{b}}{\left [ \mathbf{a,b, c} \right ]}}$ then prove that:
1. $\mathbf{a} \cdot \mathbf{a} ' = \mathbf{b} \cdot \mathbf{b} ' = \mathbf{c} \cdot \mathbf{c} ' = 1$.
2. $\left [ \mathbf{a,b, c} \right ] \left [ \mathbf{a}' , \mathbf{b}' , \mathbf{c}' \right ] = 1$.
Imagination is much more important than knowledge.

Tags:

## Create an account or sign in to join the discussion

You need to be a member in order to post a reply

## Create an account

Not a member? register to join our community
Members can start their own topics & subscribe to topics
It’s free and only takes a minute