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JEE Main & Advanced Mathematics Vector Algebra Question Bank Critical Thinking

  • question_answer
    Let the value of \[\mathbf{p}=(x+4y)\,\mathbf{a}+(2x+y+1)\,\mathbf{b}\] and \[\mathbf{q}=(y-2x+2)\,\mathbf{a}+(2x-3y-1)\,\mathbf{b},\] where a and b are non-collinear vectors. If \[3\mathbf{p}=2\mathbf{q},\] then the value of x and y will be [RPET 1984; MNR 1984]

    A) - 1, 2

    B) 2, - 1

    C) 1, 2

    D) 2, 1

    Correct Answer: B

    Solution :

    • Here,  \[3\mathbf{p}=(3x+12y)\,\mathbf{a}+(6x+3y+3)\mathbf{b}\]                                
    • \[2\mathbf{q}=(2y-4x+4)\,\mathbf{a}+(4x-6y-2)\,\mathbf{b}\]                   
    • On comparing, we get \[3x+12y=2y-4x+4\]                   
    • Þ    \[7x+10y=4\]                         -..(i)                   
    • and \[2x+9y=-5\]                          -..(ii)                   
    • On solving equations, we get \[x=2,\,\,-1.\]


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