JEE Mains · Maths · STD 12 - 11. three dimension geometry
The foot of perpendicular of the point \((2,0,5)\) on the line \(\frac{x+1}{2}=\frac{y-1}{5}=\frac{z+1}{-1}\) is \((\alpha, \beta, \gamma)\). Then. Which of the following is \(NOT\) correct?
- A \(\frac{\alpha \beta}{\gamma}=\frac{4}{15}\)
- B \(\frac{\alpha}{\beta}=-8\)
- C \(\frac{\beta}{\gamma}=-5\)
- D \(\frac{\gamma}{\alpha}=\frac{5}{8}\)
Answer & Solution
Correct Answer
(C) \(\frac{\beta}{\gamma}=-5\)
Step-by-step Solution
Detailed explanation
\(L : \frac{ x +1}{2}=\frac{ y -1}{5}=\frac{ z +1}{-1}=\lambda\) (let) Let foot of perpendicular is \(P (2 \lambda-1,5 \lambda+1,-\lambda-1)\) \(\overline{ PA }=(3-2 \lambda) \hat{ i }-(5 \lambda+1) \hat{ j }+(6+\lambda) \hat{ k }\) Direction ratio of line…
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