Geometry

# 3D Coordinate Geometry - Perpendicular Planes

Which of the following planes is perpendicular to the plane that contains the points $(0,0,0), (3,2,2 ), (6,-3,-10)?$

If the plane $a x + b y + 3z = 1$ is perpendicular to the planes \begin{aligned} -3 x + 4 y - 2 z &= 0 \\ 2 x - 3 y &= 5, \end{aligned} what is the value of $a + b ?$

Which of the following planes is perpendicular to the plane $-2x + 3 y -5 z = 1?$

Which of the following planes is perpendicular to the plane $2x - 7 y + 6 z = 6?$

$\alpha, \beta \text{ and } \gamma$ are planes such that $\alpha$ and $\beta$ do not intersect and $\alpha$ and $\gamma$ are perpendicular. Given that lines $l, m \text{ and } n$ lie on planes $\alpha, \beta \text{ and } \gamma,$ respectively, which of the following statement(s) is(are) true?

I. $\beta$ and $\gamma$ are perpendicular.
II. There exist $m$ and $n$ that intersect.
III. If $l \text{ and }m$ are perpendicular to $\gamma$, then $l // m.$

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