Q105 / 170 · Manipal (MET) 2016 · Mathematics

The equation of the plane through the points $(2,3,1)$ and $(4,-5,3)$ parallel to $X$-axis is

  • Correct answer
    A
    $y+4 z=7$
  • B
    $y+4 z=-7$
  • C
    $y-4 z=7$
  • D
    $x+4 z=7$

Solution

We know that the equation of a plane parallel to $X$-axis is $\text { by }+c z+d=0 \text {. }$ Since, it passes through the points $(2,3,1)$ and $(4,-5,3)$. $\begin{array}{lr}\therefore & 3 b+c+d=0 \\ \text { and } & -5 b+3 c+d=0\end{array}$ $\begin{array}{ll}\Rightarrow & \frac{b}{1-3}=\frac{c}{-8}=\frac{d}{14} \\ \Rightarrow & \frac{b}{-2}=\frac{c}{-8}=\frac{d}{14}\end{array}$ $\therefore$ Equation of plane is $-2 y-8 z+14=0$ i.e. $y+4 z=7$.

Hence, the correct answer is option: 'A'.

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