Vectors-

could you give me a simple definition AND example of:

1) standard Representation

2) Component Form

3) Zero vector

??

Relevance
• 7 years ago

Simply, a quantity which has both a magnitude and a direction is called a vector. For example force and momentum in physics are vectors. We consider the general dimension n for the following:

1) The standard representation is " bold v " = (a_1) j_1 + (a_2) j_2 + ... + (a_n) j_n where j_i are unit vectors in independent directions spanning the vector space, and a_i is a scalar (number) indicating the magnitude of the vector in the j_i direction.

2) The component form is < a_1, a_2, ... , a_n > -- Note that we use pointy brackets by tradition.

3) You get this when the magnitude of the vector is zero.

Example: v = 3 i + 4 j is a vector in dimension 2 written in standard form with i and j unit vectors in the direction of the x and y axes respectively. The component form is v = <3, 4>.

We always denote vectors by bold letters, or normal letters and an overhead arrow. When the starting point of the vector is not specified, it is taken to be the origin of the coordinate system.