JEE Mains · Maths · STD 12 - 11. three dimension geometry
If for \(a >0,\) the feet of perpendiculars from the points \(A ( a ,-2 a , 3)\) and \(B (0,4,5)\) on the plane \(l x+m y+n z=0\) are points \(C(0,-a,-1)\) and \(D\) respectively, then the length of line segment \(CD\) is equal to
- A \(\sqrt{31}\)
- B \(\sqrt{41}\)
- C \(\sqrt{55}\)
- D \(\sqrt{66}\)
Answer & Solution
Correct Answer
(D) \(\sqrt{66}\)
Step-by-step Solution
Detailed explanation
C lies on plane \(\Rightarrow-m a-n=0 \Rightarrow \frac{m}{n}=-\frac{1}{a} \ldots .(1)\) \(\overline{ CA } \| l \hat{ i }+ m \hat{ j }+ n \hat{ k }\) \(\frac{a-0}{l}=\frac{-a}{m}=\frac{4}{n} \Rightarrow \frac{m}{n}=-\frac{a}{4}\) \(....(2)\) From \((1) \& (2)\)…
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