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  • Please Solve R.D.Sharma class 12 Chapter 28 The Plane Exercise 28.13 Question 3 Maths textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 28 The Plane  Exercise 28.13 Question 3  Maths textbook Solution.

Answers (1)

Answer:x+y+z=0

Hint: use simultaneous equation to solve

Given:\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1} and     the point \left ( 0,7,-7 \right )

Solution: let the equation of the plane passing through \left ( 0,7,-7 \right ) be

a\left ( 2-0 \right )+b\left ( y-7 \right )+c\left ( 2+7 \right )=0 -----------(1)

The line \frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}passes through \left ( -1,3-2 \right ) and its direction ratios     are proportional to -3,2,1

Since plane (1) contains this line, it must pass through the point -3,2,1

                      \begin{aligned} &=a(-1-0)+b(3-7)+c(-2+7)=0 \\ &=-1-4 b+5 c=0 \\ &=a+4 b-5 c=0 \end{aligned}......(2)

Since plane (1) contains this line, it must be parallel to the line

                     =-3a+2b+c=0............(3)

Solving (1)(2) and (3) we get

                                  \begin{aligned} &\left(\begin{array}{ccc} x-0 & y-7 & z+7 \\ 1 & 4 & -5 \\ -3 & 2 & 1 \end{array}\right)=0 \\ &=14 x+14(y-7)+14(z+7)=0 \\ &=14 x+14 y+14 z=0 \\ &=x+y+z=0 \end{aligned}

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