question_answer

If \[\vec{A},\,\,\vec{B}\]and\[\vec{C}\] are non-zero vectors and \[\vec{A}.\,\,\vec{B}\,\,=0\] and\[\vec{B}\,.\,\vec{C}=0\], then find out the value of \[\vec{A}\].\[\vec{C}\]

Answer:

                As \[\vec{A}.\,\,\vec{B}\,\,=0\] ;              \[\therefore \,\]\[\text{AB cos}\theta =\text{ }0\]        or                \[\text{cos}\theta =0\]                 or         \[\theta =\text{9}0{}^\circ \] Similarly, \[\vec{B}\,.\,\vec{C}=0\]\[\therefore \,\]\[\text{BC cos}{{\theta }_{\text{1}}}=\text{ }0\]or \[\text{cos}{{\theta }_{\text{1}}}=\text{ }0\]or \[{{\theta }_{1}}=\text{9}0{}^\circ \] i.e. \[\vec{A}\] and \[\vec{C}\] are parallel to each other. \[\therefore \,\]\[\vec{A}.\vec{C}=\text{AC cos}0{}^\circ =\text{AC}\].