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MA 371 - Vector Norm: Dot Product
In this dot product worksheet, students solve 6 short answer problems. Students find unit vectors in the same direction as a given vector. Students express vectors as a linear combination of the standard basis vectors. Students find a...
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Applications of the Cross Product and Dot Product
In this cross product and dot product worksheet, high schoolers solve 2 problems including finding the magnetic field between 2 poles of a magnet and determining angles between vectors in a word problem about television watching given a...
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Worksheet 8 - Vectors
In this vector worksheet, students find the area of a parallelogram spanned by vectors, they give the geometric and algebraic definitions of the dot product and describe a sequence of vectors. This one-page worksheet contains six...
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Math 212: Dot Product and Cross Product
In this dot product worksheet, students consider vectors, find the value of an angle, and confirm the area of a given parallelogram. This two-page worksheet contains three problems.
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Multivariable Calculus: Dot Product
In this dot product learning exercise, students identify the properties of the dot product. They sketch vectors and obtain expressions for diagonals. This two-page learning exercise contains examples and explanations with two problems.
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Math 224 Spring 2004: Dot Product
In this dot product worksheet, students consider two vectors and compute the dot product and cross product of the given vectors. This two-page worksheet contains four problems.
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Linear Systems: Lengths and Dot Products
In this dot product worksheet, students explore the multiplication of vectors. This two-page worksheet contains explanations, examples, and approximately ten problems.
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Worksheet 4 - Geometric Mean
In this geometric worksheet, students examine the geometric and algebraic definition of the dot product. They find angles between two curves, determine if two vectors are parallel, and explain conditions on vectors. This one-page...
EngageNY
Expected Value of a Discrete Random Variable
Discover how to calculate the expected value of a random variable. In the seventh installment of a 21-part module, young mathematicians develop the formula for expected value. They connect this concept the dot product of vectors.
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Worksheet 22 - Functions
In this function worksheet, students use functions to identify an electron traveling along a path. They examine the velocity vector and compute the directional derivative. This two-page worksheet contains six multi-step problems.
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Alignment of a Solar Panel: Dot and Cross Products
In this dot and cross product learning exercise, students identify vector points under given conditions determine vertical support and determine angles of an object. This two-page learning exercise contains two problems.
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Linear Systems
In this multiplication of vectors activity, students prove that the dot product operation is commutative. They normalize a vector so it has the same direction with a magnitude of one. Students use the angle formula to confirm orthogonality.
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Lengths and Dot Sequences
In this math learning exercise, students examine the process of multiplying vectors to find their products. They practice finding the geometric and algebraic views for the solutions.
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Worksheet 20
In this math worksheet, students investigate the given vectors. Then they apply the knowledge to prove the formula for the triangle formed by them.
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Worksheet 21
In this math worksheet, students draw two vectors u and v based at the same point. The vectors are considered neither parallel nor orthogonal.
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Worksheet 31
In this math learning exercise, students investigate vectors and polar coordinates. They convert the paths of polar coordinates to Euclidian points.
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Linear Systems: Orthogonal Matrices
In this orthogonal matrices worksheet, students explore characteristics of an orthogonal matrix. They use Gram-Schmidt to convert linearly independent vectors to orthonormal vectors. This three-page worksheet contains approximately six...
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MT-A315 Introduction to Linear Algebra
In this algebra activity, students figure out the equation of the general vector, they find the orthogonal basis and apply the formula to solve the problems.
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Energy, Work and Power
In this energy, work and power worksheet, students solve 12 problems about circuits, electric motors, Ohm's Law and electric currents.