TS EAMCET · Maths · Straight Lines
A plane meets the coordinate axes at \(A, B, C\) so that the centroid of the triangle \(A B C\) is \((1,2,4)\). Then, the equation of the plane is
- A \(x+2 y+4 z=12\)
- B \(4 x+2 y+z=12\)
- C \(x+2 y+4 z=3\)
- D \(4 x+2 y+z=3\)
Answer & Solution
Correct Answer
(B) \(4 x+2 y+z=12\)
Step-by-step Solution
Detailed explanation
The equation of the plane meets the coordinate axes at \(A, B, C\) is \(\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1\) \(\ldots\) (i) Let \(\quad O A=a, O B=b, O C=c\) Also, the centroid of \(\triangle A B C\) is \(\left(\frac{a}{3}, \frac{b}{3}, \frac{c}{3}\right)\). which is equal to…
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