JEE Main & Advanced Sample Paper JEE Main Sample Paper-26

  • question_answer
    If the angle between the plane \[x-3y+2z=1\] and the line \[\frac{x-1}{2}=\frac{y-1}{1}=\frac{z-1}{-3}\] is \[\theta \], then the value of \[\cos ec\theta \] is

    A)  1                    

    B)  2

    C)  3                                

    D)  4  

    Correct Answer: B

    Solution :

    Vector normal to the plane is \[\vec{n}=\hat{i}-3\hat{j}+2\hat{k}\] and  vector along the line is \[\vec{V}=2\hat{i}+\hat{j}-3\hat{k}\] Now \[\sin \theta =\frac{n.v}{|n||v|}\,=\left| \frac{2-3-6}{\sqrt{14}\,\sqrt{14}} \right|\,=\left| \frac{7}{14} \right|\] Hence \[\cos ec\,\theta =2\]

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