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

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

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Answer:-  The required equation of the plane is 4x-3y+2z-3=0

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:- (0,-1,0), (3,3,0) and (1,1,1)

Solution:- We know that, the equation of the plane passing through given three 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}{lll} 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

Now, substitute the given value

\begin{aligned} &\Rightarrow\left|\begin{array}{ccc} x-0 & y+1 & z-0 \\ 3-0 & 3+1 & 0-0 \\ 1-0 & 1+1 & 1-0 \end{array}\right|=0 \\\\ &\Rightarrow\left|\begin{array}{lll} x & y+1 & z \\ 3 & 4 & 0 \\ 1 & 2 & 1 \end{array}\right|=0 \end{aligned}

\begin{gathered} (x)(4-0)-(y+1)(3-0)+z(6-4)=0 \\\\ 4 x-(y+1)(3)+z((2)=0 \\\\ 4 x-3 y-3+2 z=0 \\\\ \therefore 4 x-3 y+2 z-3=0 \end{gathered}

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