question_answer

Can a vector be zero when one of the components is not zero while all the other components are zero?

Answer:

                No. Any vector \[\vec{A}\] in three dimensions can be written as \[\vec{A}={{A}_{x}}\hat{i}+{{A}_{y}}\hat{j}+{{A}_{z}}\hat{k}\] Where \[A=\sqrt{A_{x}^{2}+A_{y}^{2}+A_{z}^{2}}\] Clearly, if any of the components \[{{A}_{x}},{{A}_{y}}\]or \[{{A}_{z}}\] is not zero, the vector \[\vec{A}\] will not be a zero vector.