The components of a vector are its magnitude or length, and its direction. They can be represented as x and y coordinates in a two-dimensional plane, or as x, y, and z coordinates in a three-dimensional space.
The magnitude of a vector can be found using the Pythagorean theorem, which states that the square of the hypotenuse (the length of the vector) is equal to the sum of the squares of its components (x and y or x, y, and z).
A scalar is a quantity that has only magnitude, such as speed or temperature. A vector, on the other hand, has both magnitude and direction, such as velocity or force. Scalars can be represented by a single number, while vectors require multiple components.
To add or subtract vectors, you can use the parallelogram method or the head-to-tail method. In the parallelogram method, you draw the two vectors as adjacent sides of a parallelogram and the diagonal represents the resultant vector. In the head-to-tail method, you draw the first vector and then draw the second vector starting from the tip of the first vector. The resultant vector is the one that connects the tail of the first vector to the head of the second vector.
A position vector represents the location of a point in space relative to an origin, while a displacement vector represents the change in position of an object from its initial position to its final position. A displacement vector can be thought of as a specific type of position vector, as it also has magnitude and direction.