Measurements and Standards
There is a way of comparing units of measurement. They may be designated by magnitude or by magnitude and direction. We are given these terms: scalars and vectors. Scalars denote magnitude; vectors denote magnitude and direction.
Comparing things, for example, velocity to speed, they may seem the same in one respect and different in another. Speed and velocity are not one and the same. Speed is a scalar, whereas velocity is a vector.
Representation of Displacement as Vectors
This concept seems to make sense. For example, we may think of someone's pushing of a block as how much force somebody used to push a block, and in what direction he pushed it.
The method of vector addition that is most methodical is to separate the x and y components of the vector (the left and right, and the up and down components -- break into horizontal and vertical components) and add all the x's together and add all the y's together...then use the Pythagorean theorem to find the magnitude (since, after all, they form a right triangle and the magnitude is the hypotenuse).
Thus, if you visualize it as a right triangle, the x and y component would correspond to the triangle's legs, more specifically the adjacent and opposite sides. Then, with tanØ to find the angle of the magnitude (direction it is point at).
Vector subtraction is very similar to vector addition (the adding of components is the same). Simply, the difference between them is in their signs. In vector subtraction, the vectors are pointing in opposite directions, thus canceling out to some degree (i.e. if one direction is considered positive, it's opposite direction is considered negative).
Graphical Resolution of Vectors [head to tail and parallelogram]
This is a situation in which all the vector components cancel each other out, resulting in no net vector (i.e., a vector of 0).
Java Interactions and Demonstrations