The scalar product and the vector product
The scalar (dot) product of two vectors is a number that tells us the angle between them; the vector (cross) product is a vector perpendicular to both. Work out both and use them.
- UK: Year 12
- France: grade 11
- Germany: grade 12
- Iran: grade 12
- Afghanistan: grade 11
- Syria: grade 11
- Palestine: grade 11
- Ukraine: grade 10
- Russia: grade 9
Guide
This studio follows the last two lessons of Afghan Year 11 chapter 7, Iran's Year 12 geometry chapter 3 and Further Maths. The scalar product (dot product) of two vectors is a number: multiply matching components and add them with their signs. It equals |a||b|cosθ, where θ is the angle between the vectors. If the product is zero the vectors are perpendicular.
The vector product (cross product) of two vectors is a vector perpendicular to both. We write it as a 3 × 3 determinant whose first row is i, j and k; the j component takes a minus sign. Its length is the area of the parallelogram the two vectors make.
Common mistakes: losing the signs of negative components, and forgetting the minus sign on the j component of a cross product.