Vector definition,addition subtraction and scalar multiplication
Key examples for solid understanding of
Vector definition,addition subtraction and scalar multiplication
The scalar product(dot product, inner product) of 2 vectors
Vector projection and example
Cross product of 2 vectors
Lines and planes
4 key aspects about lines and planes:
1.Equations: vector form, parametric form and Cartesian form, conversion between different forms, find the equations(ie,give 2 points to find the equation of a line, give 3 points to find the equation of a plane, give 2 lines to find the equation of a plane, give a equation of a plane to find another plane which is parallel to the given plane).
2.Intersections: line and line, line and plane, plane and plane. Line and line could have no intersection because they are parallel or skew. To find the intersection between a line and plane, just plug the parametric format of the line to the Cartesian equation of the plane. 3 planes may intersect at one point(unique solution), one line(infinite number of solutions) or no intersection(no solution)
3.Distances: point to line, point to plane, line to line, plane to plane. To find the distance from a point to a line, we can use the parametric format of the line equation to represent a position vector on the line,with the dot product of this position vector and the line's direction vector = 0, we can find the nearest point on the line. Distances of point to plane, line to line, plane to plane have simple formulas which we will discuss in the following slides.
4.Angles: between 2 lines, a line and a plane, 2 planes. We will discuss in the last slide.
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