Plane vectors
Read one plane vector as a position, a direction, or coordinates, and use the same picture for a projection, a dot product, a basis, and a normal.
Plane vectors
6 pieces about this concept, across works, topic guides, and exam visualizations.
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Topics
Works
Vector addition and scalar multiplication
Add two plane vectors by the parallelogram rule, and scale one of them, to see how a linear combination is built.
Geometric significance of the dot product
The dot product, or inner product, reads the angle between two vectors, a right angle, and the work of a force.
Vector projection
Split a vector into a part along a chosen direction and a part at right angles to it, and drag to see the length change with the angle.
Exam visualizations
Center on the x-axis, a distance ratio, and tangent slopes
115 AST Mathematics I, Fill-in 10: a circle with center on the x-axis is fixed by a ratio of distances to two perpendicular lines, then the slopes of the tangents through the origin are found.
Parallelogram area with the edge directions fixed
114 AST Mathematics I, Fill-in 11: the sides stay on two fixed directions, and the area is read from the vector between the center and one vertex.