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| Pre-calculus
Contents I |
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Vectors in a Plane and
Space |
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Vectors
in a Plane |
Vectors - introduction |
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Length, magnitude or
norm of the vector |
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Collinear, opposite
and coplanar vectors |
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Addition of vectors |
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Triangle rule (law)
and parallelogram rule |
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Zero or null vector |
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Subtraction of vectors |
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Scalar multiplication
or multiplication of a vector by scalar |
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Unit vector |
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Addition, subtraction
and scalar multiplication of vectors, examples |
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Linear combination of
vectors |
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Linear dependence of
vectors |
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Vectors
and a coordinate system, Cartesian vectors |
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Vectors in
a coordinate plane (a two-dimensional system of coordinates), Cartesian
vectors |
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Radius vector or position vector |
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Vector components |
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Vectors in
a two-dimensional system examples |
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Vectors in
three-dimensional space in terms of Cartesian coordinates |
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Angles of
vectors in relation to coordinate axes, directional cosines - scalar
components of a vector |
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The unit vector of a vector |
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Vectors in
a three-dimensional coordinate system examples |
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Scalar product or dot
product or inner product |
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Orthogonality or
perpendicularity of two vectors |
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Different positions of two vectors and the corresponding values of
the scalar product |
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Square of magnitude of
a vector |
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Scalar product of unit
vectors |
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Scalar or dot
product properties |
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Scalar product in the
coordinate system |
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Angle between vectors
in a coordinate plane |
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Projection of a vector in the direction of another vector,
the scalar and vector components |
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Vector
product or cross product |
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Vector
product |
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Right-handed system |
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An example for the vector product in physics |
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The condition for two vectors to be parallel |
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The vector products of the standard unit vectors |
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The vector product properties |
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The vector product in
the component form |
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The mixed product
or the scalar triple product |
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The mixed product
or scalar triple product definition |
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The
mixed product properties |
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The condition for
three vectors to be coplanar |
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The mixed product
or scalar triple product expressed in terms of components |
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The vector product
and the mixed product use, examples |
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| Pre-calculus Contents |
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