JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let two vertices of triangle \(ABC\) be \((2,4,6)\) and \((0,-2,-5)\), and its centroid be \((2,1,-1)\). If the image of third vertex in the plane \(x+2 y+4 z=11\) is \((\alpha, \beta, \gamma)\), then \(\alpha \beta+\beta \gamma+\gamma \alpha\) is equal to
- A \(72\)
- B \(74\)
- C \(76\)
- D \(70\)
Answer & Solution
Correct Answer
(B) \(74\)
Step-by-step Solution
Detailed explanation
Given, \(A(2,4,6), B (0,-2,-5)\) \(G (2,1,-1)\) Let vertex \(C ( x , y , z )\) \(\frac{2+0+x}{3}=2 \Rightarrow x=4\) \(\frac{4-2+y}{3}=1 \Rightarrow y=1\) \(\frac{6-5+z}{3}=-1 \Rightarrow z=-4\) Third vertex, \(C(4,1,-4)\) Then image of vertex in the plane let image…
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