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JEE Main & Advanced Sample Paper JEE Main Sample Paper-18

  • question_answer
    Let \[{{P}_{1}}=\vec{r},\,\,{{\vec{r}}_{1}}={{d}_{1}},\]\[{{P}_{2}}=\vec{r}.\,{{\vec{r}}_{2}}={{d}_{2}},\]\[{{P}_{3}}=\vec{r}.\,{{\vec{r}}_{3}}={{d}_{3}}\]be three planes where \[\vec{r},\,\,{{\vec{r}}_{2}}\] and \[{{\vec{r}}_{3}}\] are three non-coplanar vectors. Then the lines \[{{P}_{1}}=0={{P}_{2}};\]\[{{P}_{2}}=0={{P}_{3}};\] and\[{{P}_{3}}=0={{P}_{1}}\]are

    A)  parallel lines                     

    B)  coplanar lines

    C)  coincident lines               

    D)  concurrent lines

    Correct Answer: D

    Solution :

     Lines\[{{P}_{1}}=0={{P}_{2}};\,{{P}_{2}}=0={{P}_{3}};\]and\[{{P}_{3}}=0={{P}_{1}}\] are lines of intersection of planes \[{{P}_{1}}\] and \[{{P}_{2}}:{{P}_{2}}\] and \[{{P}_{3}},\,{{P}_{3}}\] and\[{{P}_{1}}\]respectively Therefore, the lines are non-coplanar and will intersect at unique point.


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