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- https://math.libretexts.org/Bookshelves/Calculus/Vector_Calculus_(Corral)/01%3A_Vectors_in_Euclidean_Space/1.05%3A_Lines_and_PlanesNow that we know how to perform some operations on vectors, we can start to deal with some familiar geometric objects, like lines and planes, in the language of vectors. The reason for doing this is s...Now that we know how to perform some operations on vectors, we can start to deal with some familiar geometric objects, like lines and planes, in the language of vectors. The reason for doing this is simple: using vectors makes it easier to study objects in 3-dimensional Euclidean space. We will first consider lines.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/01%3A_Systems_of_Equations/1.01%3A_Systems_of_Linear_Equations/1.1E%3A_Exercises_for_Section_1.1This page offers exercises on solving linear systems graphically, focusing on finding intersection points of lines, understanding different solution scenarios (no, unique, infinite solutions), and exa...This page offers exercises on solving linear systems graphically, focusing on finding intersection points of lines, understanding different solution scenarios (no, unique, infinite solutions), and examining common intersections of multiple lines or planes. It includes a word problem involving weights of four individuals and tasks requiring the construction of linear systems with defined solution properties and graphical relationships.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/04%3A_RThis page details vector concepts, covering operations like dot and cross products, lines and planes in R3, and spanning sets. It discusses linear independence, matrix spaces (row, colum...This page details vector concepts, covering operations like dot and cross products, lines and planes in R3, and spanning sets. It discusses linear independence, matrix spaces (row, column, null), orthogonal vectors/matrices, the Gram-Schmidt process for orthonormal sets, orthogonal projections, and least squares approximation. The page includes exercises for practice at the end of each section.
