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JEE Mains · Maths · STD 12 - 11. three dimension geometry
The distance of the point \((1,-5, 9)\) from the plane \(x - y + z = 5\) measured along the line \(x = y = z\) is
- A \(\frac{{10}}{{\sqrt 3 }}\)
- B \(\frac{{20}}{3}\)
- C \(3\sqrt {10} \)
- D \(\;10\sqrt 3 \)
Answer & Solution
Correct Answer
(D) \(\;10\sqrt 3 \)
Step-by-step Solution
Detailed explanation
Equation of line parallel to \(x=y=z\) through \((1,-5,9)\) is \(\frac{x-1}{1}=\frac{y+5}{1}=\frac{z-9}{1}=\lambda\) If \(\mathrm{P}(\lambda+1, \lambda-5, \lambda+9)\) be point of intesection of line and plane. \(\Rightarrow \lambda+1-\lambda+5+\lambda+9=5\)…
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