The equation of plane containing z-axis and passing through the point(1,2,3) is:

x = 2 y - z

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2 x = y

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9 x = 6 y - 7 z = 0

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x + 2 y - z = 0

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Solution

The correct option is B $x = 2 y - z$
The plane contains z-axis and the point $(1, 2, 3)$

Any plane which contains z-axis is of $(0, 0, 1)$
$∴$ By cross product of the two points we can find the equation.
$∴ ∣ ∣ ∣ ∣ \begin{matrix} x & y & z 0 & 0 & 1 1 & 2 & 3 \end{matrix} ∣ ∣ ∣ ∣ = 0$
$\Rightarrow - 2 x + y = 0$
$\Rightarrow y = 2 x o r 2 x = y$ (ans.)

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