A lesson on applying the scalar product of two vectors

Abstract

In their mathematics education, the Bulgarian students encounter vectors for the first time in the 8th grade. There, they get to know the concept of a vector – a directed segment, study collinear and non-collinear vectors, same direction and opposite direction vectors, equality of vectors, opposite vectors and the zero vector. The affine operations with vectors are introduced – addition, subtraction and multiplication of a vector by a number.

According to the new program for profiled preparation in mathematics in the 11th grade, the concept of scalar product of two vectors and operations on vectors with coordinates in a Cartesian coordinate system are introduced. Students’ knowledge in problems related to vectors is strengthened. They can now add, multiply, find the length of vectors that are set with coordinates. Students are introduced to the application of vectors in analytical geometry, in solving problems with polygons and stereometric problems. We know that the application of the vector apparatus is enormous, so we present solving algebra and calculus problems by using the already familiar vector operations.