Principles of vector calculus
Collinear vectors. Coplanar vectors. Equality of vectors. Parallel
transfer of vectors. Addition of vectors. Subtraction of vectors.
Laws of addition of vectors. Laws of multiplication of vector by a
number. Scalar product of vectors. Angle between non-zero vectors.
Scalar square. Properties of a scalar product. Unit orthogonal vectors.
Coordinates of a vector. Algebraic operations with vectors. Vector
product of vectors. Properties of a vector product. Necessary and
sufficient condition of collinearity of vectors. Necessary and sufficient
condition of coplanarity of vectors.
Necessaryand sufficient condition of collinearity of vectors a = ( x, y, z ) and b = ( u, v, w ) :