3D Coordinate Geometry

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

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

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

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 $P ?$

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

Concept Quizzes

Challenge Quizzes

3D Coordinate Geometry - Distance

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.