AP EAMCET · Maths · Three Dimensional Geometry
A plane passes through the point \((3,5,7)\). If the direction ratios of its normal are equal to the intercepts made by the plane \(x+3 y+2 z=9\) with the coordinate axes, then the equation of that plane is
- A x + y + z = 5
- B 6x + 2 y + 3z = 105
- C 12 x + 4y + 6z = 49
- D 6x + 2 y + 3z = 49
Answer & Solution
Correct Answer
(D) 6x + 2 y + 3z = 49
Step-by-step Solution
Detailed explanation
Given equation of plane. \[ \begin{aligned} x+3 y+2 z & =9 \\ \Rightarrow \quad \frac{x}{9}+\frac{y}{3}+\frac{z}{\left(\frac{9}{2}\right)} & =1 \end{aligned} \] \(\Rightarrow\) So, intercepts are \(9,3, \frac{9}{2}\). According to the questions, direction ratio of normal is…
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