Waste less time on Facebook — follow Brilliant.
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, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Geometry
3D Coordinate Geometry
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, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Your answer seems reasonable.
Find out if you're right!
Sign up to access problem solutions.
That seems reasonable.
Find out if you're right!
Concept Quizzes
What is the distance between the point \(P=(1,-2,3)\) and the plane \(x-2y+3z-28=0?\)
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, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Your answer seems reasonable.
Find out if you're right!
Sign up to access problem solutions.
That seems reasonable.
Find out if you're right!
by Brilliant Staff
What is the shortest distance between the point \(P=(-3,3,2)\) and the sphere \(x^2+(y-6)^2+(z+1)^2=1?\)
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, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Your answer seems reasonable.
Find out if you're right!
Sign up to access problem solutions.
That seems reasonable.
Find out if you're right!
by Brilliant Staff
Find the square of distance between the point \( M_{0}(0, 1, 3) \) and the line \[\frac{ x-4 }{2} = y-7 = \frac{ z+1}{2}. \]
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, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Your answer seems reasonable.
Find out if you're right!
Sign up to access problem solutions.
That seems reasonable.
Find out if you're right!
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 \(P ?\)
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, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Your answer seems reasonable.
Find out if you're right!
Sign up to access problem solutions.
That seems reasonable.
Find out if you're right!
by Brilliant Staff
What is the square of the distance between the two lines \[\begin{align} l&:~x-9=y-8=z-4,\\ m&:~x-10=y-10=z-7? \end{align}\]
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, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Your answer seems reasonable.
Find out if you're right!
Sign up to access problem solutions.
That seems reasonable.
Find out if you're right!
by Brilliant Staff