# dot product verification

• March 10th 2009, 12:11 PM
dopi
dot product verification
is the dot product of (a+b) . (a + b) = a^2 + b^2 + 2ab ?
• March 10th 2009, 02:26 PM
Prove It
Quote:

Originally Posted by dopi
is the dot product of (a+b) . (a + b) = a^2 + b^2 + 2ab ?

No, it's just $a^2 + b^2$.

You only do componentwise multiplication with dot products.
• March 10th 2009, 02:48 PM
Plato
Quote:

Originally Posted by dopi
is the dot product of (a+b) . (a + b) = a^2 + b^2 + 2a.b ?

That is more or less correct!
But it should be written as $\left( {a + b} \right) \cdot \left( {a + b} \right) = a \cdot a + 2a \cdot b + b \cdot b$.
In fact here is an important form: $\left( {a + b} \right) \cdot \left( {a + b} \right) = \left\| a \right\|^2 + 2a \cdot b + \left\| b \right\|^2$

Quote:

Originally Posted by Prove It
No, it's just $a^2 + b^2$.
You only do componentwise multiplication with dot products.

No that is not correct!
To see where you went wrong, recall $v \cdot \left( {u + w} \right) = v \cdot u + v \cdot w$.
Let $v = \left( {a + b} \right)\;,\,u = a\;\& \,w = b$ and apply the distribution rule twice.