C.5 VectorsHL
HL only. Vectors as directed quantities — position vectors anchored at the origin, displacement vectors free to translate, base vectors i, j, k. Magnitude formula |v| = √(x² + y² + z²) (Pythagoras in 3D). Vector arithmetic (sums, differences, scalar multiples) component-wise. Midpoint formula m = (a + b)/2 and applications to collinearity proofs. Subsequent lessons cover scalar product, vector equation of a line, cross product and planes, and intersections of lines/planes.
Vectors — position, displacement, magnitude, base vectorsHLSign up
Vectors as directed quantities — position vs displacement, base vectors · Vector arithmetic and magnitudes
Scalar (dot) productHLSign up
Definition: a · b = |a| |b| cos θ · Angle between vectors; perpendicular and parallel detection
Vector equation of a lineHLSign up
Vector form r = a + λb; convert to Cartesian · Constant-velocity kinematics; angle between two lines
Cross product and planesHLSign up
Coincident, parallel, intersecting, skew lines · Cross product a × b · Vector and Cartesian equations of a plane
Intersections of lines and planesHLSign up
Line-plane and plane-plane intersections · Angles between planes; distance from point to plane