Question

The length of the vector $\overline{AG}=\frac{1}{3}i+\frac{7}{3}j+\frac{1}{3}k$ is

• A. $\sqrt{17}$
• B. $\sqrt{51}/3$
• C. $\sqrt{51}/9$
• D. $\sqrt{59}/4$

Answer 1

The correct option is B $\sqrt{51}/3$

Given vector

$\overrightarrow{AG}=\frac{1}{3}\hat{i}+\frac{7}{3}\hat{j}+\frac{1}{3}\hat{k}$

to find the length we can calculate magnitude

$\left|\overrightarrow{AG}\right|=\sqrt{(\frac{1}{3}{)}^2+(\frac{7}{3}{)}^2+(\frac{1}{3}{)}^2}$

$\left|\overrightarrow{AG}\right|=\sqrt{\frac{1}{9}+\frac{49}{9}+\frac{1}{9}}$

$\left|\overrightarrow{a}\right|=\sqrt{\frac{51}{9}}$

$\left|\overrightarrow{a}\right|=\frac{\sqrt{51}}{3}$