AP EAMCET · Maths · Three Dimensional Geometry
\(\mathrm{G}(1,0,1)\) is the centroid of the triangle ABC. If \(\mathrm{A}=(1,-4,2)\) and \(\mathrm{B}=(3,1,0)\) then \(\mathrm{AG}^2+\mathrm{CG}^2=\)
- A \(\mathrm{BG}^2\)
- B \(2 \mathrm{BG}^2\)
- C \(6 \mathrm{BG}^2\)
- D \(5 \mathrm{BG}^2\)
Answer & Solution
Correct Answer
(D) \(5 \mathrm{BG}^2\)
Step-by-step Solution
Detailed explanation
\(C_x = 3(1) - (1+3) = -1\) \(C_y = 3(0) - (-4+1) = 3\) \(C_z = 3(1) - (2+0) = 1\) \(C=(-1,3,1)\) \(AG^2 = (1-1)^2 + (0-(-4))^2 + (1-2)^2 = 0+16+1 = 17\) \(CG^2 = (1-(-1))^2 + (0-3)^2 + (1-1)^2 = 4+9+0 = 13\) \(AG^2+CG^2 = 17+13 = 30\)…
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