Simple Point Vector

A vector describes a movement from one point to another. A vector quantity has both direction and magnitude size.

In this section we will introduce some common notation for vectors as well as some of the basic concepts about vectors such as the magnitude of a vector and unit vectors. We also illustrate how to find a vector from its staring and end points.

A Vector An example of a vector. Vectors are usually represented by arrows with their length representing the magnitude and their direction represented by the direction the arrow points. Vectors require both a magnitude and a direction. The magnitude of a vector is a number for comparing one vector to another.

I understand that a vector has direction and magnitude whereas a point doesn't. However, in the course notes that I am using, it is stated that a point is the same as a vector. Also, can you do cross product and dot product using two points instead of two vectors? I don't think so, but my roommate insists yes, and I'm kind of confused now.

A vector is a mathematical entity that has magnitude as well as direction. It is used to represent physical quantities like distance, acceleration, etc. Learn the vectors in math using formulas and solved examples.

A vector whose x -displacement is a and whose y -displacement is b will have terminal point a, b when the initial point is the origin, 0, 0. This leads us to a definition of a standard and concise way of referring to vectors.

We have turned a point into a vector. By definition, vectors of the same length and pointing in the same direction are the same vectors. These vectors are said to be equal. So, the two vectors depicted in Figure 1.3.1.3, are exactly the same vector. Vector addition is the shown in 5 and is purely component-wise operation.

Vector Representation A vector in a plane is represented by a directed line segment an arrow. The endpoints of the segment are called the initial point and the terminal point of the vector. An arrow from the initial point to the terminal point indicates the direction of the vector. The length of the line segment represents its magnitude.

For example, in a plane, a vector can have infinitely many directions, corresponding to the infinite lines passing through a point, with each direction line having two opposite orientations. The length of the directed segment is called the magnitude and is denoted by placing the name of the vector between two vertical bars.

It still points in the same direction, but is 3 times longer And now you know why numbers are called quotscalarsquot, because they quotscalequot the vector up or down. Multiplying a Vector by a Vector Dot Product and Cross Product How do we multiply two vectors together? There is more than one way! The scalar or Dot Product the result is a scalar.