question_answer

What will be the difference in product of (i) real number with a vector (ii) scalar with a vector.

Answer:

                If\[\theta \] is the angle between \[\vec{A}\]and \[\vec{B}\],                                                                    Then \[C={{\left( {{A}^{2}}+{{B}^{2}}+2AB\cos \theta  \right)}^{1/2}}=\left( A+B \right)\]                                                                                                              [Given] \[\therefore \]  \[{{A}^{2}}+{{B}^{2}}+2AB\cos \theta ={{\left( A+B \right)}^{2}}={{A}^{2}}+2AB+{{B}^{2}}\] or            \[\cos \theta =1\]                            or            \[\theta ={{0}^{o}}\]