Question

Compute the magnitude of the following vectors:$\overrightarrow{a}$=$\hat{i}$+$\hat j+\hat k$;$\overrightarrow{b}$=2$\hat{i}$-7$\hat{j}$-3$\hat{k}$; $\overrightarrow{c}$= $\frac{1}{\sqrt 3}\hat i+\frac{1}{\sqrt 3}\hat j-\frac{1}{\sqrt 3}\hat k$

Answer 1

The given vectors are: :$\overrightarrow{a}$=$\hat{i}$+$\hat j+\hat k$;$\overrightarrow{b}$=2$\hat{i}$-7$\hat{j}$-3$\hat{k}$; $\overrightarrow{c}$= $\frac{1}{\sqrt 3}\hat i+\frac{1}{\sqrt 3}\hat j-\frac{1}{\sqrt 3}\hat k$

|$\overrightarrow{a}$| =$\sqrt {(1)^2+(1)^2+(1)^2}$=$√3$

|$\overrightarrow{b}$| =$\sqrt{(2)^2+(-7)^2+(-3)^2} = \sqrt{4+49+9}$

=$√62$

|$\overrightarrow{c}$| = $\sqrt{(\frac {1}{√3})^2+(\frac{1}{√3})^3+(\frac {-1}{√3}})^2$

= $\sqrt{(\frac {1}{√3})+(\frac{1}{√3})+(\frac {-1}{√3}})$ =1