MHT CET · Maths · Three Dimensional Geometry
Equation of plane containing the line \(\frac{x}{2}=\frac{y}{3}=\frac{z}{4}\) and perpendicular to the plane containing the lines \(\frac{x}{3}=\frac{y}{4}=\frac{z}{2}\) and \(\frac{x}{4}=\frac{y}{2}=\frac{z}{3}\) is
- A \(x+2 y+z=0\)
- B \(x+2 y-z=0\)
- C \(x-2 y+z=0\)
- D \(x-2 y-\mathrm{z}=0\)
Answer & Solution
Correct Answer
(C) \(x-2 y+z=0\)
Step-by-step Solution
Detailed explanation
Equation of the plane containing \(\frac{x}{3}=\frac{y}{4}=\frac{z}{2}\) and \(\frac{x}{4}=\frac{y}{2}=\frac{z}{3}\) is
\(
\begin{aligned}
& \left|\begin{array}{ccc}
x & y & z \\
3 & 4 & 2 \\
4 & 2 & 3
\end{array}\right|=0 \\
& \Rightarrow 8 x-y-10 z=0
\end{aligned}
\)
Now required plane is perpendicular to this plane.
Consider option (C)
\(
(8)(1)+(-1)(-2)+(-10)(1)=0
\)
\(
\begin{aligned}
& \left|\begin{array}{ccc}
x & y & z \\
3 & 4 & 2 \\
4 & 2 & 3
\end{array}\right|=0 \\
& \Rightarrow 8 x-y-10 z=0
\end{aligned}
\)
Now required plane is perpendicular to this plane.
Consider option (C)
\(
(8)(1)+(-1)(-2)+(-10)(1)=0
\)
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