KVPY Sample Paper KVPY Stream-SX Model Paper-22

  • question_answer
    If \[\vec{p}=3\vec{a}-5\vec{b}\,\,;\]\[\vec{q}=2\vec{a}+\vec{b}\,\,;\]\[\vec{r}=\vec{a}+4\vec{b}\,\,;\]\[\vec{s}=-\,\vec{a}+\vec{b}\] are four vectors such that \[\sin \,(\vec{p}\wedge \vec{q})=1\] and \[\sin \,(\vec{r}\wedge \vec{s})=1\]then \[\cot \,(\vec{a}\wedge \vec{b})\] is:

    A) \[-\frac{19}{5\sqrt{43}}\]

    B) 0

    C) \[\frac{19}{5\sqrt{43}}\]

    D) 1

    Correct Answer: C

    Solution :

    \[\vec{p}\cdot \vec{q}=0\] & \[\vec{r}\cdot \vec{s}=0.\]Form two simultaneous equations and get a relation between \[|\vec{a}|\] & \[|\vec{b}|\] as \[25|\vec{a}{{|}^{2}}=43|\vec{b}{{|}^{2}}.\] now compute \[({{\vec{a}}^{\wedge }}\vec{b})=\frac{\vec{a}\cdot \vec{b}}{|\vec{a}||\vec{b}|}\]

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