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Geometry

3D Coordinate Geometry

Concept Quizzes

3D Coordinate Geometry - Distance
3D Coordinate Geometry - Equation of a Line
3D Coordinate Geometry - Skew Lines
3D Coordinate Geometry - Equation of a Plane
3D Coordinate Geometry - Parallel Planes
3D Coordinate Geometry - Perpendicular Planes
3D Coordinate Geometry - Intersection of Planes
Equation of a sphere
3D Section Formula
3D Coordinate Geometry - Problem Solving

Challenge Quizzes

3D Coordinate Geometry: Level 2 Challenges
3D Coordinate Geometry: Level 3 Challenges

3D Coordinate Geometry - Perpendicular Planes

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

2 x + 3 y - 3z = 12

3 x - y + 2 z = 8

3 x +2 y +2 z = 1

4 x + 2 y + z = 1

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by Brilliant Staff

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 $a + b ?$

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by Brilliant Staff

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

-5 x + 2 y + 3 z = 4

x - y + z = 4

2 x -2y - 2z = 3

3 x - 2 y + 5 z = 2

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by Brilliant Staff

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

- 7 x + - y - 9 z = 13

- 8 x - 7 y + 4 z = 13

- 13 x + 4 y + 9 z = 4

13 x - 4 y - 13 z = 4

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by Brilliant Staff

$\alpha, \beta \text{ and } \gamma$ 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 $l // m.$

I only I and II only II and III only I, II and III

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by Brilliant Staff