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Excel in math and science
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Geometry
Dot Product of Vectors
Excel in math and science
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It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
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Concept Quizzes
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Find the shortest distance between the point \(P=(1,-2,3)\) and the line \[2(x-3)=y-1=z+1.\]
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.
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by Brilliant Staff
Find the shortest distance between the point \(P=(0,3,4)\) and the line \[x=0,\ \frac{y}{2}=-z+3.\]
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
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Our wiki is made for math and science
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by Brilliant Staff
Find the shortest distance between the origin and the line \[x-1=\frac{y+1}{-4}=\frac{z-7}{3}.\]
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,
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Used and loved by 4 million people
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by Brilliant Staff
What is the shortest distance between the line \(x-2=y-1=z+1\) and the sphere \(x^2+y^2+z^2=4?\)
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,
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by Brilliant Staff
Find the shortest distance between the origin and the line \[\frac{x+1}{2}=-y+2=-z+2.\]
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.
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That seems reasonable.
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by Brilliant Staff