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JEE Main & Advanced Mathematics Vector Algebra Question Bank Vector or Cross product of two vectors and its application

  • question_answer
    If the position vectors of three points \[A,B\] and \[C\] are respectively i + j + k, 2i + 3j ? 4k and 7i + 4j + 9k, then the unit vector to the plane containing the triangle \[ABC\] is                                                 [DCE 1999]

    A)                 31i ? 18j ? 9k

    B)                 \[\frac{31i-38j-9 k}{\sqrt{2486}}\]

    C)                 \[\frac{31i+18j+9k}{\sqrt{2486}}\]

    D)                 None of these

    Correct Answer: B

    Solution :

               Unit vector perpendicular to plane of \[\Delta ABC\] is, \[\frac{\overrightarrow{AB}\times \overrightarrow{AC}}{|\overrightarrow{AB}\times \overrightarrow{AC}|}\],                    where \[\overrightarrow{AB}=i+2j-5k\] and \[\overrightarrow{AC}=6i+3j+8k\]            \ \[\overrightarrow{AB}\times \overrightarrow{AC}=31i-38j-9k\]and \[|\overrightarrow{AB}\times \overrightarrow{AC}|\,=\sqrt{2486}\]                 \ Required vector = \[\frac{31i-38j-9k}{\sqrt{2486}}\].


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