Length of U . V

Thank you both!! 

Length of v is √( (-2)² + 0² + 1²) = √(4+0+1) = √5 

$${\sqrt{{\mathtt{5}}}} = {\mathtt{2.236\: \!067\: \!977\: \!499\: \!789\: \!7}}$$

If the last part is meant to be the length of the vector sum of u and v, then you have to sum the components first, before calculating the length, not add the lengths of the individual vectors together.

u+v = (-1, 2, 4)

length of u+v = √( (-1)² + 2² + 4²) = √21

$${\sqrt{{\mathtt{21}}}} = {\mathtt{4.582\: \!575\: \!694\: \!955\: \!84}}$$

u= (1, 2, 3)    

v= (-2, 0, 1) 

$$\vec{w}=\vec{u}+\vec{v} = \left( \begin{array}{c} 1 & 2 & 3 \end{array} \right) +\left( \begin{array}{c} -2 & 0 & 1 \end{array} \right) = \left( \begin{array}{c} 1-2 & 2+0 & 3+1 \end{array} \right) = \left( \begin{array}{c} -1 & 2 & 4 \end{array} \right)$$

$$\begin{array}{rcl} \|w\| &=& \sqrt{(-1)^2+2^2+4^2} \\\\ &=&\sqrt{1+4+16}\\\\ &=&\sqrt{21}\\\\ & \approx & 4.58257569496 \end{array}$$