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Excel in math and science
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Properties of a Vector
Vectors allow you to represent quantities with both size and direction, such as the velocity of an airplane. Better yet, they do so in a mathematically-useful way. Dive in to see how!
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.
Concept Quizzes
Challenge Quizzes
Find the magnitude of the vector \(\vec{v}=(-3,4)?\)
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,
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.
Point P lies on side BC and divides it internally in the ratio 1 : 4 in the equilateral triangle \(ABC\) below. Let \(\vec{AB}=\vec{a},\) \(\vec{AC}=\vec{b},\) \(\vec{AP}=\vec{c}.\) Then \(\vec{c}\) can be expressed as \(x\vec{a}+y\vec{b}.\) Which of the following is equal to \(x\times y\)?
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
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\(G\) is the centroid of triangle \(OAB\) below. Let \(\vec{OA}=\vec{a}, \vec{OB}=\vec{b},\) and \(\vec{GA}=\vec{c}\). Then \(\vec{c}\) can be expressed as \(x\vec{a}-y\vec{b}.\) Which of the following is equal to \(x - y\)?
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
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A commercial airliner can fly at a cruising velocity of 250m/s without the influence of the wind. If a 30m/s gust continuously blows 70\(^\circ\) south of east, then how many degrees north of east should the pilot angle the plane thereby counteracting the speed of the wind so that the plane flies directly east?
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
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including olympiad champions, researchers, and professionals.
Let the position vectors of three points \(A, B,\) and \(C\) be \(\vec{a}, \vec{b},\) and \(\vec{c},\) respectively. Then \(2\vec{AB}+3\vec{BC}-\vec{CA}\) can be expressed as \(x\vec{a}+y\vec{b}+z\vec{c}.\) Calculate \(x^2+y^2+z^2\).