# Dot product error?

I'm trying to figure out the dot product $a \cdot b$ of the following vectors:

$\vec a = 2 \hat i - \hat j + \hat k$

$\vec b = 3 \hat i + 3 \hat j - 3 \hat k$

Here's my working out:

$|\vec a| = \sqrt{2^2+ (-1)^2 + 1^2} = \sqrt 6$

$|\vec b| = \sqrt{3 + 3^2 + (-3)^2} = \sqrt 3$

Therefore:

$\vec a \cdot \vec b = 2^2 \times 3^2 + (-1)^2 \times 3^2 + 1^2 \times (-3)^2 = 18$

I'm sure this isn't correct, what have I missed or done wrong?

Please feel free to edit my text so it looks more suitable. Thanks in advance.

• You don't need to square the coordinates before taking the dot product. – lEm Mar 30 '16 at 6:48
• You don't calculate dot products that way. – Nikunj Mar 30 '16 at 6:48
• You seem to appreciate formula jam. What you wrote is full of mistakes, try to be more rigorous. – Yves Daoust Mar 30 '16 at 6:49
• Actually helping > critisim – toadflax Mar 30 '16 at 6:58

Your definition of the dot product is wrong, given to vecors $$a = xi + yj + zk$$ and $$b = ui + vj + wk\text{.}$$ $a\cdot b$ is defined as $$a\cdot b = ux+yv+zw$$
Also, note that $$\left|a\right| = \sqrt{x^2+y^2+z^2} = \sqrt{xx+yy+zz} = \sqrt{a\cdot a}$$ which is what you have used in your intermediate step.