1.6.2—Vector product
- Syllabus
- 9231–2028–2029
- Objective
- 1.6.2
- Level
- AS
The vector product gives a perpendicular vector and its area magnitude
The vector or cross product a×b is perpendicular to both a and b, with magnitude |a×b|=|a||b|sinθ. Its magnitude is the area of the parallelogram spanned by the two vectors.
The order reverses direction: a×b=−(b×a). It is zero when vectors are parallel, so it can test parallelism and construct a plane normal.
(1,0,0)×(0,2,0)=(0,0,2), whose magnitude 2 is the area of the rectangle formed by the vectors.
The cross product is not a scalar dot product, and changing the order is not harmless.
ConceptA-Level CAIE Further Math AS