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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 - Distance

What is the distance between the point $P=(1,-2,3)$ and the plane $x-2y+3z-28=0?$

5\sqrt{6}

2\sqrt{14}

4\sqrt{6}

1\sqrt{14}

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by Brilliant Staff

What is the shortest distance between the point $P=(-3,3,2)$ and the sphere $x^2+(y-6)^2+(z+1)^2=1?$

3\sqrt{3}-1

5-3\sqrt{3}

2\sqrt{2}-1

5-2\sqrt{2}

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by Brilliant Staff

Find the square of distance between the point $M_{0}(0, 1, 3)$ and the line $\frac{ x-4 }{2} = y-7 = \frac{ z+1}{2}.$

32

576

192

64

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by Brilliant Staff

If the distance of a point $P$ other than the origin from the plane $x+y+z=3$ is equal to the distance of the plane from the origin, which of the following can be the point $P ?$

(6,-3,6)

(0,6,-3)

(3,6,0)

(6,3,-3)

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by Brilliant Staff

What is the square of the distance between the two lines $\begin{aligned} l&:~x-9=y-8=z-4,\\ m&:~x-10=y-10=z-7? \end{aligned}$

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by Brilliant Staff

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