TS EAMCET · Maths · Three Dimensional Geometry
If a plane cuts the coordinate axes at \(A, B\) and \(C\) respectively such that the centroid of the triangle \(A B C\) is \((6,6,3)\), then the equation of that plane.
- A \(x+y+z=18\)
- B \(x+2 y+z=18\)
- C \(x+y+2 z=18\)
- D \(2 x+y+z=18\)
Answer & Solution
Correct Answer
(C) \(x+y+2 z=18\)
Step-by-step Solution
Detailed explanation
Let the equation of plane is \[ \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1 \] Centroid of triangle formed by the coordinates axes at \((a, 0,0),(0, b, 0)\) and \((0,0, c)\) is \(\left(\frac{a}{3}, \frac{b}{3}, \frac{c}{3}\right)\) Given…
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