Vectors in the Plane
A vector is a line segment running from point A (tail) to point B (head).
Each vector has a magnitude (also referred to as length) and a direction.
Direction of a Vector
This is the direction of the line which contains the vector or any line which is parallel to it.
Magnitude of a Vector
The magnitude of the vector is the length of the line segment . It is denoted by .
The magnitude of a vector is always a positive number or zero.
The magnitude of a vector can be calculated if the coordinates of the endpoints are known:
Calculate the magnitude of the following vectors:
Calculate the value of k knowing the magnitude of the vector = (k, 3) is 5.
The vector that joins the coordinates origin, O, with a point, P, is the position vector of the point P.
Components or Coordinates of a Vector
If the coordinates of A and B are:
Find the components of the vector :
The vector has the components (5, −2). Find the coordinates of A if the terminal point is known as B(12, −3).
Calculate the coordinates of Point D so that the quadrilateral of Points: A(−1, −2), B(4, −1), C(5, 2) and D form a parallelogram.