If \(\overrightarrow{\mathbf{a}}\) and \(\overrightarrow{\mathbf{b}}\) are unit vectors and \(|\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}}|=1\), then \(|\overrightarrow{\mathbf{a}}-\overrightarrow{\mathbf{b}}|\) is equal to

Given, \(\quad|\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}}|=1\)
\(\therefore \quad|\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}}|^{2}=1^{2}\)
\(\Rightarrow|\overrightarrow{\mathbf{a}}|^{2}+|\overrightarrow{\mathbf{b}}|^{2}+2|\overrightarrow{\mathbf{a}}||\overrightarrow{\mathbf{b}}|=1\)
\(\Rightarrow \quad 2|\overrightarrow{\mathbf{a}}||\overrightarrow{\mathbf{b}}|=1-(1+1)\)
\(\Rightarrow \quad 2|\overrightarrow{\mathbf{a}}||\overrightarrow{\mathbf{b}}|=-1\)
Now, \(|\overrightarrow{\mathbf{a}}-\overrightarrow{\mathbf{b}}|^{2}=|\overrightarrow{\mathbf{a}}|^{2}+|\overrightarrow{\mathbf{b}}|^{2}-2|\overrightarrow{\mathbf{a}}||\overrightarrow{\mathbf{b}}|\) \(=1^{2}+1^{2}-(-1)=3\) [from Eq. (i)] \(\Rightarrow \quad|\overrightarrow{\mathbf{a}}-\overrightarrow{\mathbf{b}}|=\sqrt{3}\)