Vectors and curves in space

Concepts

• Cross product 10 exercisesThe cross product of two vectors mathbf u and mathbf v in mathbb R^3 is the vector perpendicular to both whose length is the area…
• Lines and planes in space 10 exercisesA line in space is determined by a point mathbf r_0 and a direction vector mathbf d; a plane, by a point mathbf r_0 and a normal…
• Parametric curve 10 exercisesA parametric curve is the path traced by a point in space when its coordinates depend on a parameter t through a vector-valued fu…
• Arc length 10 exercisesThe arc length of a parametric curve mathbf r(t), with a≤ t≤ b, is the total distance L traveled along it, measured along the cur…
• Quadric surface 10 exercisesA quadric surface is the set of points (x,y,z) in space that satisfy a second-degree equation in x, y, z with real coefficients A…