JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let the image of the point \(P (1,2,3)\) in the line \(L : \frac{ x -6}{3}=\frac{ y -1}{2}=\frac{ z -2}{3}\) be \(Q .\) let \(R (\alpha, \beta, \gamma)\) be a point that divides internally the line segment \(PQ\) in the ratio \(1: 3\). Then the value of \(22(\alpha+\beta+\gamma)\) is equal to
- A \(225\)
- B \(185\)
- C \(127\)
- D \(125\)
Answer & Solution
Correct Answer
(D) \(125\)
Step-by-step Solution
Detailed explanation
Let \(M\) be the mid-point of \(PQ\) \(\therefore M =(3 \lambda+6,2 \lambda+1,3 \lambda+2)\) Now, \(\overrightarrow{ PM }=(3 \lambda+5) \hat{ i }+(2 \lambda-1) \hat{ j }+(3 \lambda-1) \hat{ k }\) \(\because \overrightarrow{ PM } \perp(3 \hat{ i }+2 \hat{ j }+3 \hat{ k })\)…
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