Vector Algebra — Class 12 Mathematics

A vector has both magnitude and direction, in contrast to a scalar. This chapter introduces position vectors, direction cosines and direction ratios, and the representation . Vectors are added by the triangle and parallelogram laws and scaled by real numbers. Two products are central: the scalar (dot) product , which measures projection and tests perpendicularity, and the vector (cross) product , whose magnitude gives the area of the parallelogram spanned by the vectors and whose direction is perpendicular to both. The unit vector and the section formula are also covered. These tools underpin three-dimensional geometry and physics.