18. explain vector product or cross product of two vectors,
19. explain and apply properties of vector product of vectors,
20. represent the vector product of two vectors in terms of its components,
1. Directed line segment is represented by a vector :
Directed line segment: A directed line segment can be represented as a vector quantity. If one end of a straight line is termed as the initial point and the other end as the terminal point then the straight line is a directed line segment. The directed line segment whose initial point is A and terminal point is B is denoted by AB. Point A is often called the "tail" of the vector, and B is called the vector's "head." AB and BA are oppositely directed line segments; because the initial and terminal points of AB are A and B and those of BA are B and A respectively. With any directed line segment AB is associated length, support and direction or sense.
2. Support of Vector, Equal Vectors, Opposite Vector, Zero Vector:
Support: The line of unlimited length of which a directed line segment is a part is called the line of support or simply support. In the figure, the line XY is the support of AB.
Sense or direction: The direction of AB is from the point A to the point B and that of BA is from the point B to the point A. Hence the direction of the directed line segment is from the initial point to the terminal point. Hence the directions of AB and BA are not the same.
Length or modulus of a Vector: The modulus of a vector is the measurement of the length of that portion of a directed line segment by which the vector is denoted. The modulus of a vector is always positive and the length of AB is denoted by |AB|.
Unit Vector: The vector whose length is unity is called a unit vector. If a vector whose magnitude is not equal to zero is divided by its magnitude we get a unit vector in the direction of the vector or in its parallel direction. If A is a vector whose magnitude is |A| where |A| ≠ 0, then A / |A| is a unit vector in the direction of the vector A or in its parallel direction. We suppose that A / |A| = â.
