question_answer

Find the conditions for two vectors to be (i) parallel and (ii) perpendicular to each other.

Answer:

                (i) If \[\vec{A}||\vec{B},\]then \[\theta ={{0}^{\circ }}\]                 and \[\vec{A}\times \vec{B}=|\vec{A}||\vec{B}|\sin {{0}^{\circ }}\hat{n}=\vec{0}\] Hence if two vectors are parallel, then their cross product must be zero. (ii) If \[\vec{A}\bot \vec{B},\] then \[\theta ={{90}^{\circ }}\] and \[\vec{A}.\vec{B}=|\vec{A}||\vec{B}|\cos {{90}^{\circ }}=0\] Hence if two vectors are perpendicular, then their dot product must be zero.