Q 34. - Calculus

Question

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

Step-by-Step Solution

Answer

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

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.

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