MATH-M 311 Lecture Notes - Lecture 4: Parallelogram, Unit Vector, Distributive Property
Document Summary
9-2-15: 2 = set of all ordered pairs of all real numbers, 3 = set of all ordered triples of all real numbers, by analogy, n exists for some. Often drawn with different starting points: can have different representations of same-magnitude vector. Warning: different directed line segments represent same vector and we refer to them all as the same name. All said to represent vector: each kind of operation with vectors has algebraic and geometric characterizations. Vector addition: if and , then, ex. If and , then: geometric interpretation of (or ): Scalar multiplication: scalar- real number, element of , if is a vector and is a scalar, then. If and , then: geometrically, vector scales (stretches/shrinks) by factor of. Magnitude- length of directed line segment (any of its representations) corresponding to a vector: notation: magnitude of, if then obtained by using distance formula in 3 dimensions assuming vector starts at origin, ex.
