VIT Engineering VIT Engineering Solved Paper-2015

  • question_answer
    If a, b and c are three non ? coplanar vectors, then (a + b ? c) . \[\left[ \left( a-b \right)\times \left( b-c \right) \right]\] equals

    A) 0                                             

    B) \[\text{a}\text{. b }\!\!\times\!\!\text{ c}\]

    C) \[\text{a}\text{. c }\!\!\times\!\!\text{ b}\]                       

    D) \[\text{3a}\text{. b }\!\!\times\!\!\text{ c}\]

    Correct Answer: B

    Solution :

    \[{{\left[ \text{Fe}{{\left( {{\text{H}}_{\text{2}}}\text{O} \right)}_{\text{6}}} \right]}^{\text{3+}}}\text{}{{\left[ \text{Fe}{{\left( \text{N}{{\text{O}}_{\text{2}}} \right)}_{\text{6}}} \right]}^{\text{3-}}}\text{}{{\left[ \text{Fe}{{\left( \text{N}{{\text{H}}_{\text{3}}} \right)}_{\text{6}}} \right]}^{\text{3-}}}\] \[\because \] \[{{\text{E}}_{\text{1}}}\text{=}{{\text{E}}_{\text{2}}}\text{=}\frac{\text{1}}{\text{4 }\!\!\pi\!\!\text{ }{{\text{ }\!\!\varepsilon\!\!\text{ }}_{\text{0}}}}\text{.}\frac{\text{q}}{{{\text{r}}^{\text{2}}}}\]     \[{{E}_{R}}=\sqrt{E_{1}^{2}+E_{2}^{2}+2{{E}_{1}}{{E}_{2}}\cos {{60}^{\circ }}}\] \[=\sqrt{E_{1}^{2}+E_{1}^{2}+2E_{1}^{2}\times \frac{1}{2}=\sqrt{3}{{E}_{1}}}\] \[\therefore \] \[{{E}_{R}}=\frac{\sqrt{3}q}{4\pi {{\varepsilon }_{0}}{{r}^{2}}}\] \[\tau =qEL\sin \theta \]


You need to login to perform this action.
You will be redirected in 3 sec spinner