Geometry

3D Coordinate 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)? (0,0,0), (3,2,2 ), (6,-3,-10)?

If the plane ax+by+3z=1 a x + b y + 3z = 1 is perpendicular to the planes 3x+4y2z=02x3y=5,\begin{aligned} -3 x + 4 y - 2 z &= 0 \\ 2 x - 3 y &= 5, \end{aligned} what is the value of a+b? a + b ?

Which of the following planes is perpendicular to the plane 2x+3y5z=1? -2x + 3 y -5 z = 1?

Which of the following planes is perpendicular to the plane 2x7y+6z=6? 2x - 7 y + 6 z = 6?

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

I. β\beta and γ\gamma are perpendicular.
II. There exist mm and nn that intersect.
III. If l and ml \text{ and }m are perpendicular to γ\gamma, then l//m. l // m.

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