Understand the rules of vector addition, subtraction, and multiplication.
Apply graphical methods of vector addition and subtraction to determine the displacement of moving objects.
Vectors in two dimensions
A
vector is a quantity that has magnitude and direction. Displacement, velocity, acceleration, and force, for example, are all vectors. In one-dimensional, or straight-line, motion, the direction of a vector can be given simply by a plus or minus sign. In two dimensions (2-d), however, we specify the direction of a vector relative to some reference frame (i.e., coordinate system), using an arrow having length proportional to the vector’s magnitude and pointing in the direction of the vector.
[link] shows such a
graphical representation of a vector , using as an example the total displacement for the person walking in a city considered in
Kinematics in Two Dimensions: An Introduction . We shall use the notation that a boldface symbol, such as
, stands for a vector. Its magnitude is represented by the symbol in italics,
, and its direction by
.
Vectors in this text
In this text, we will represent a vector with a boldface variable. For example, we will represent the quantity force with the vector
, which has both magnitude and direction. The magnitude of the vector will be represented by a variable in italics, such as
, and the direction of the variable will be given by an angle
.
Vector addition: head-to-tail method
The
head-to-tail method is a graphical way to add vectors, described in
[link] below and in the steps following. The
tail of the vector is the starting point of the vector, and the
head (or tip) of a vector is the final, pointed end of the arrow.
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form