AP EAMCET · Maths · Three Dimensional Geometry
A plane cuts the coordinate axes \(X, Y, Z\) at \(A\), \(B, C\) respectively such that the centroid of the \(\triangle A B C\) is \((6,6,3)\). Then the equation of that plane is
- A \(x+y+z-6=0\)
- B \(x+2 y+z-18=0\)
- C \(2 x+y+z-18=0\)
- D \(x+y+2 z-18=0\)
Answer & Solution
Correct Answer
(D) \(x+y+2 z-18=0\)
Step-by-step Solution
Detailed explanation
Let the equation of the plane is \[ \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1 \] By the definition of the centroi \(\left(\frac{a}{3}, \frac{b}{3}, \frac{c}{3}\right)=(6,6,3)\) Therefore, \[ \begin{aligned} a & =18 \\ b & =18 \\ c & =9 \end{aligned} \] The equation of the plane…
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