Question

Find the norm of the vector.$v=\left(\frac{1}{2},\frac{1}{3},\frac{1}{4}\right)$

Short answer

The norm of the vector $v=\left(\frac{1}{2},\frac{1}{3},\frac{1}{4}\right)$is $\sqrt{\frac{61}{144}}$.

Step-by-step solution

Step 1. Given information .  

We have given vector$v=\left(\frac{1}{2},\frac{1}{3},\frac{1}{4}\right)$

Step 2. Find the norm of the vector. 

$$\begin{gathered} ||v||=\sqrt{a^2+b^2+c^2} \\ =\sqrt{{\left(\frac{1}{2}\right)}^2+{\left(\frac{1}{3}\right)}^2+{\left(\frac{1}{4}\right)}^2} \\ =\sqrt{\frac{1}{4}+\frac{1}{9}+\frac{1}{16}} \\ =\sqrt{\frac{36+16+9}{144}} \\ =\sqrt{\frac{61}{144}} \end{gathered}$$