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  • Please solve RD Sharma class 12 chapter The Plane exercise 28.1 question 1 sub question (i) maths textbook solution

Please solve RD Sharma class 12 chapter The Plane exercise 28.1 question 1 sub question (i) maths textbook solution

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Answer:-  The required equation of the plane is 7x+3y-z=17

Hint:- Use equation of the plane \left(x_{1}, y_{1}, z_{1}\right),\left(x_{2}, y_{2}, z_{2}\right) and \left(x_{3}, y_{3}, z_{3}\right)

Given:-  (2,1,0), (3,-2,-2) and (3,1,7)

Solution:-  We know that, the equation of the plane passing through three non-collinear points \left(x_{1}, y_{1}, z_{1}\right),\left(x_{2}, y_{2}, z_{2}\right) and \left(x_{3}, y_{3}, z_{3}\right) is

\left|\begin{array}{ccc} x-x_{1} & y-y_{1} & z-z_{1} \\ x_{2}-x_{1} & y_{2}-y_{1} & z_{2}-z_{1} \\ x_{3}-x_{1} & y_{3}-y_{1} & z_{3}-z_{1} \end{array}\right|=0

\begin{aligned} &\Rightarrow\left|\begin{array}{ccc} x-2 & y-1 & z-0 \\ 3-2 & -2-1 & -2-0 \\ 3-2 & 1-1 & 7-0 \end{array}\right|=0 \\\\ &\Rightarrow\left|\begin{array}{ccc} x-2 & y-1 & z \\ 1 & -3 & -2 \\ 1 & 0 & 7 \end{array}\right|=0 \end{aligned}

\begin{gathered} (x-2)(-21)-(y-1)(9)+z(3)=0 \\\\ \therefore 7 x+3 y-z=17 \end{gathered}

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