If a unit vector is represented by $$0.5\hat i + 0.8\hat j + c\hat k,$$    then the value of $$c$$ is

Solution :
Concept
Unit vector can be found by dividing a vector with its magnitude i.e. $$\hat A = \frac{A}{{\left| A \right|}}$$
Let we represent the unit vector by $$\hat n.$$ We also know that the modulus of unit vector is 1 i.e., $$\left| {\hat n} \right| = 1$$
$$\eqalign{ & \therefore \left| {\hat n} \right| = \left| {0.5\hat i + 0.8\hat j + c\hat k} \right| = 1 \cr & {\text{or}}\,\,\sqrt {{{\left( {0.5} \right)}^2} + {{\left( {0.8} \right)}^2} + {c^2}} = 1 \cr & {\text{or}}\,\,0.25 + 0.64 + {c^2} = 1 \cr & {\text{or}}\,\,0.89 + {c^2} = 1 \cr & {\text{or}}\,\,{c^2} = 1 - 0.89 = 0.11 \Rightarrow c = \sqrt {0.11} \cr} $$