VIT Engineering VIT Engineering Solved Paper-2015

  • question_answer
    If (2, 7, 3) is one end of a diameter of the sphere \[{{\text{x}}^{\text{2}}}\text{+}{{\text{y}}^{\text{2}}}\text{+}{{\text{z}}^{\text{2}}}\text{-6x-12y-2z+20=0}\], then the coordinates of the other end of the diameter are

    A) (-2, 5, -1)                             

    B) (4, 5, 1)

    C)  (2, -5, 1)                             

    D) (4, 5, -1)

    Correct Answer: D

    Solution :

    Given equation of sphere is \[Q=ms\Delta \theta =0.1\times 250\times 0.4\] Centre \[2C\times {{10}^{4}}=10\] If one of the end of diameter is (2, 7, 3). Let the other end of the diameter be (x, y, z). \[\Rightarrow \]        \[C=\frac{10}{2\times {{10}^{4}}}=5\times {{10}^{-4}}\] \[\therefore \]        2 + x = 6 \[C=500\mu F\]       x = 4              7 + y = 12 \[{{C}_{0}}=\frac{{{\varepsilon }_{0}}A}{d}=3\mu F\]       y = 5 and      3 + z = 2 \[{{\varepsilon }_{r}}\]       z = - 1 Therefore, (x, y, z)  \[C=\frac{K{{\varepsilon }_{0}}A}{d}=15\mu F\] (4, 5, - 1)


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