TS EAMCET · Maths · Three Dimensional Geometry
If the equation of the plane passing through the point \((2,-3,4)\) and perpendicular to both the planes \(2 x-3 y+5 z=2\) and \(x+y+2 z=3\) is \(x+p y+q z=r\), then \(r\) is equal to
- A \(\frac{5}{11}\)
- B \(\frac{45}{11}\)
- C \(\frac{-1}{11}\)
- D \(\frac{39}{11}\)
Answer & Solution
Correct Answer
(A) \(\frac{5}{11}\)
Step-by-step Solution
Detailed explanation
Equation of plane passing through \((2,-3,4)\) having \(\operatorname{DR}^{\prime} s(a, b, c)\) is given by \( a \cdot(x-2)+b(y+3)+c(z-4)=0 \) \(\therefore \Rightarrow \quad a x+b y+c z-2 a+3 b-4 c=0\) ...(i) Since, Eq. (i) is perpendicular to both the planes \(2 x-3 y+5 z=2\)…
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