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Properties of a Vector
Excel in math and science
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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,
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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
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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?
NOTE: "South of east" and "north of east" are terms used in bearing; imagine a pointer straight east, and the rotates some angle clockwise (that's south of east) or counterclockwise (that's north of 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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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 \(x^2+y^2+z^2\).