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BCECE Engineering BCECE Engineering Solved Paper-2011

  • question_answer
     A vector which makes equal angle with the vectors \[1/3(i-2j+2k),1/5(-4i-3k)\]and j is

    A)  \[5i+j+jk\]                            

    B)         \[-6i+j+5k\]         

    C)                         \[5i-j-5k\]                             

    D)         \[5i+j-5k\]

    Correct Answer: C

    Solution :

    Let the required vector be \[a=xi+yj+zk.\]It makes equal angles with the vectors \[b=\frac{1}{3}(i-2j+2k)\] \[c=\frac{1}{5}(-4i-3k),d=j\]                 \[\therefore \]\[a.b=a.c=a.d\][\[\because \] b, c, d are unit vectors]                 If \[a.b=a.d,\]then                                 \[\frac{1}{3}(x-2y+2z)=y\]                 If \[a.c=a.d,\]then                                 \[\frac{1}{5}(-4x-3z)=y\]                 \[\Rightarrow \]    \[x-5y+2z=0\]                 and         \[4x+5y+3z=0\] Solving these equation, we get \[x=-z\]and \[x=-5y\]                 \[\therefore \]      \[\frac{x}{-5}=\frac{y}{1}=\frac{z}{5}\]                 \[\Rightarrow \]    \[\frac{x}{5}=\frac{y}{-1}=\frac{z}{-5}\]                 \[\therefore \]      \[a=-5i+j+5k\]                 or            \[a=5i-j-5k\]


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