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KVPY Sample Paper KVPY Stream-SX Model Paper-7

  • question_answer
    Let A be a point on the line \[\vec{r}=(1-3\mu )\hat{i}+(\mu -1)\hat{j}+(2+5\mu )\hat{k}\] and B (3, 2,6) be a point in the space. Then the value of \[\mu \] for which the vector \[\overset{\xrightarrow{{}}}{\mathop{AB}}\,\] is parallel to the plane \[x-4y+3z=1\] is:

    A) \[\frac{1}{4}\]                          

    B)  \[\frac{1}{8}\]

    C) \[\frac{1}{2}\]                          

    D) \[-\frac{1}{4}\]

    Correct Answer: A

    Solution :

    Let A is\[(1-3\mu ,\mu -1,2+5\mu )\]
    \[\overrightarrow{AB}=(3\mu +2)i+(3-\mu )j+(4-5\mu )\]
    \[\hat{k}\]which is parallel to plane \[x-4y+3z=1\]
    \[\Rightarrow \]   \[1(3\mu +2)-4(3-\mu )+3(4-5\mu )=0\]
    \[\Rightarrow \]               \[-8\mu +2=0\]
    \[\Rightarrow \]               \[\mu =\frac{1}{4}\]


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