TS EAMCET · Maths · Three Dimensional Geometry
A plane meets the coordinate axes at \(P, Q, R\) respectively. If the centroid of \(\triangle P Q R\) is \(\left(1, \frac{1}{2}, \frac{1}{3}\right)\), then the equation of the plane is
- A \(2 x+4 y+3 z=5\)
- B \(x+2 y+3 z=3\)
- C \(x+4 y+6 z=5\)
- D \(2 x-2 y+6 z=3\)
Answer & Solution
Correct Answer
(B) \(x+2 y+3 z=3\)
Step-by-step Solution
Detailed explanation
Let the equation of the plane be \(\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1\) Since, plane meets the coordinate axes at \(P, Q, R\) respectively. So, the coordinates of the points \(P, Q, R\) are \((a, 0,0),(0, b, 0),(0,0, c)\) respectively. Also, centroid of \(\triangle P Q R\) is…
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