Question

If $\overrightarrow{a}\mathrm{and}\overrightarrow{b}$are mutually perpendicular unit vectors, write the value of $\left|\overrightarrow{a}+\overrightarrow{b}\right|.$

Answer 1

$$\begin{gathered} \overrightarrow{a}\text{and}\overrightarrow{b}\text{are unit vectors and they are perpendicular.} \\ \Rightarrow \left|\overrightarrow{a}\right|=\left|\overrightarrow{b}\right|=1;\overrightarrow{a}.\overrightarrow{b}=0...\left(\mathrm{i}\right) \\ \text{Now,} \\ {\left|\overrightarrow{a}+\overrightarrow{b}\right|}^2={\left|\overrightarrow{a}\right|}^2+{\left|\overrightarrow{b}\right|}^2+2\overrightarrow{a}.\overrightarrow{b} \\ =1+1+2\left(0\right)\left[\mathrm{Using}\left(\mathrm{i}\right)\right] \\ =2 \\ \therefore \left|\overrightarrow{a}+\overrightarrow{b}\right|=\sqrt{2} \end{gathered}$$