Final answer:
Vector notation can be expressed by its components, such as 4, -3, or using unit vectors, such as 4.0(-î) + 3.0(j). The negative of a vector has the same magnitude but opposite direction, which is crucial for operations like vector subtraction, represented as A - B = A + (-B).
Step-by-step explanation:
Understanding Vector Notation
When expressing a vector, there are multiple notations you can use. One common notation involves listing its components, such as 4, -3, which implies a vector with an x-component of 4 and a y-component of -3. The x-component of a vector, represented as Ďx = -4.0, means that the vector has an x-component magnitude of 4.0 units and points in the negative direction of the x-axis. Hence, in a typical coordinate system, this vector points to the left. The notation 4.0(-î) also represents a vector with a magnitude of 4.0 in the negative x-direction, where î indicates a unit vector along the x-axis with a magnitude of 1.
Vector subtraction is another key concept. Subtracting vector B from vector A is the same as adding the negative vector -B to A, denoted as A - B = A + (-B). The negative of a vector is simply a vector of the same magnitude but pointing in the opposite direction. For example, if B is a vector, then -B is the vector with the same length as B but pointing in the opposite direction. This is useful for visualizing vector operations and understanding the direction and magnitude of vectors resulting from these operations.
To use two different notations to describe a vector with an x-component of -4 and a y-component of 3, one could write (-4, 3) or 4.0(-î) + 3.0(j), where j is the unit vector in the y-direction. Both notations provide the magnitude and direction of each component of the vector.