question_answer

The dot product of two vectors vanishes when vectors are orthogonal and has maximum value when vectors are parallel to each other. Explain.            

Answer:

                We know that \[\vec{A}\,.\,\vec{B}=\text{AB cos}\theta \]; when vectors are orthogonal, \[\theta =\text{9}0{}^\circ \]; So,\[\vec{A}\,.\,\vec{B}\] = AB cos 90o= 0 When vectors are parallel, \[\theta =0{}^\circ \]; So, \[\vec{A}\,.\,\vec{B}=\text{AB cos}0{}^\circ =\text{AB }\left( \text{Max}. \right)\]