Compute the magnitude of the following vectors:
$\vec{a}=\hat{i} + \hat{j}+\hat{k;}$ $ \vec{b}=2\hat{i}-7\hat{j}-3\hat{k};$ $ \vec{c}=\frac{1}{\sqrt{3}}\hat{i}+\frac{1}{\sqrt{3}}\hat{j}-\frac{1}{\sqrt{3}}\hat{k}$
Answer
The given vectors are:$\vec{a}=\hat{i} + \hat{j}+\hat{k;}$ $ \vec{b}=2\hat{i}-7\hat{j}-3\hat{k};$ $\vec{c}=\frac{1}{\sqrt{3}}\hat{i}+\frac{1}{\sqrt{3}}\hat{j}-\frac{1}{\sqrt{3}}\hat{k};$
$\Big|\vec{a}\Big|=\sqrt{(1)^2+(1)^2+(1)^2}=\sqrt{3}$
$\Big|\vec{b}\Big|=\sqrt{(2)^2+(-7)^2+(-3)^2}$
$=\sqrt{4+49+9}$
$=\sqrt{62}$
$\Big|\vec{c}\Big|=\sqrt{\bigg(\frac{1}{\sqrt{3}}\bigg)^2+\bigg(\frac{1}{\sqrt{3}}\bigg)^2+\bigg(-\frac{1}{\sqrt{3}}\bigg)^2}$
$=\sqrt{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}=1$