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# 3D Coordinate Geometry

Append a z-axis to the 2-dimensional plane and conquer the realm of 3-dimensional space.

\end{align}\]
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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