2. Solved Papers
  3. WB JEE Medical

WB JEE Medical WB JEE Medical Solved Paper-2014

  • question_answer
    Consider three vectors \[A=\hat{i}+\hat{j}-2\hat{k},\,\]\[B=\hat{i}-\hat{j}+\hat{k}\]and \[C=2\hat{i}-3\hat{j}+4\hat{k}.\]A vector X of the form \[\alpha A+\beta B\](\[\alpha \] and\[\beta \] are numbers) is perpendicular to C. The ratio of \[\alpha \]and \[\beta \] is

    A) 1:1

    B)  2:1

    C)  -1:1           

    D)  3:1

    Correct Answer: A

    Solution :

    Vector X of the form \[\alpha A+\beta B\] \[X=\alpha A+\beta B\] \[=\alpha (\hat{i}+\hat{j}-2\hat{k})+\beta (\hat{i}-\hat{j}+\hat{k})\] \[X=\hat{i}(\alpha +\beta )+\hat{j}(\alpha -\beta )+\hat{k}(-2\alpha +\beta )\]A vector X is perpendicular to C, ie., \[X-C=0\]\[[\hat{i}(\alpha +\beta )+\hat{j}(\alpha -\beta )]\] \[+\hat{k}(-2\alpha +\beta )].\]\[[2\hat{i}-3\hat{j}+4\hat{k}]=0\] or    \[2(\alpha +\beta )-3(\alpha -\beta )+4(-2\alpha +\beta )=0\] or    \[2\alpha +2\beta -3\alpha +3\beta -8\alpha +4\beta =0\] or \[-9\alpha +9\beta =0\]or \[\alpha =\beta \] or \[\frac{\alpha }{\beta }=\frac{1}{1}\]or \[\alpha :\beta =1:1\]


You need to login to perform this action.
You will be redirected in 3 sec spinner