question_answer

The resultant of two vectors \[\vec{A}\] and \[\vec{B}\]perpendicular to the vector \[\vec{A}\]and its magnitude is equal to half of the magnitude of the vector\[\vec{B}\]. Find out the angle between \[\vec{A}\] and \[\vec{B}\]

Answer:

                No A vector \[\vec{A}\]in three dimensions can be written as \[\vec{A}={{\text{A}}_{\text{x}}}\text{i }+\text{ }{{\text{A}}_{\text{y}}}\text{j }+\text{ }{{\text{A}}_{\text{z}}}\text{k}\]; where\[A=\sqrt{A_{x}^{2}+A_{y}^{2}+A_{z}^{2}}\] Therefore, if any of \[{{\text{A}}_{\text{x}}},{{\text{A}}_{\text{y}}},{{\text{A}}_{\text{z}}}\] is not zero, vector \[\vec{A}\]cannot be zero. It means a vector can be zero only if all its components are zero.