J & K CET Engineering J and K - CET Engineering Solved Paper-2007

  • question_answer
    Through the point \[P(\alpha ,\,\beta ,\,\,\gamma )\] a plane is drawn at right angles to OP to meet the coordinate axes are A, B,. C respectively. If \[OP=p,\]then equation of plane \[\underset{ABC}{\longleftrightarrow}\] is

    A)  \[\alpha x+\beta y+\gamma z=p\]

    B)  \[\frac{x}{\alpha }+\frac{x}{\beta }+\frac{z}{\gamma }=p\]

    C)  \[2\alpha x+2\beta y+2\gamma z={{p}^{2}}\]

    D)  \[\alpha x+\beta y+\gamma z={{p}^{2}}\]

    Correct Answer: A

    Solution :

    Equation of plane is  \[\vec{r}\,.\hat{n}=d\] Where d is the perpendicular distance of the  plane from origin.                          \[\Rightarrow \] \[\alpha x+\beta y+\gamma z=0\]


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