Question

Find the norm of the vector. $v=\left(\frac{1}{3},\frac{1}{3},-\frac{1}{3}\right)$

Short answer

The norm of the vector$v=\left(\frac{1}{3},\frac{1}{3},-\frac{1}{3}\right)$is$\sqrt{\frac{1}{3}}$.

Step-by-step solution

Step 1. Given information .  

We have given vector$v=\left(\frac{1}{3},\frac{1}{3},-\frac{1}{3}\right)$.

Step 2. Find the norm of the vector.  

$$\begin{gathered} ||v||=\sqrt{a^2+b^2+c^2} \\ =\sqrt{{\left(\frac{1}{3}\right)}^2+{\left(\frac{1}{3}\right)}^2+{\left(\frac{1}{3}\right)}^2} \\ =\sqrt{\frac{1}{9}+\frac{1}{9}+\frac{1}{9}} \\ =\sqrt{\frac{3}{9}} \\ =\sqrt{\frac{1}{3}} \end{gathered}$$