Final answer:
The components of a vector A are technically understood as its magnitude and direction, aligning with option A of the question. In a Cartesian coordinate system, vector components refer to the vector's projections on the x and y axes, named Ax and Ay. The magnitude of a vector is deduced from the square root of the sum of the squares of its components, and its direction can be calculated using trigonometry.
Step-by-step explanation:
The components of vector A are its magnitude and direction, which technically means option A) Magnitude and direction is correct. However, if we are discussing the representation of a vector in a coordinate system, the vector's components refer to the projections of the vector along the coordinates axes, typically labeled as Ax and Ay for the x and y-axis, respectively. These are also known as the rectangular components of a vector.
Vector Components and Scalar Components
Vector components of a vector are the two parts that point in either the x or y direction in a two-dimensional space. On the other hand, the scalar components of a vector are the differences in coordinates between the origin and endpoint of the vector.
Magnitude and Direction Angle
The magnitude of a vector is defined as the square root of the sum of the squares of its components, which follows from the Pythagorean theorem. To identify the direction angle of a vector in a plane, we often use trigonometric functions to calculate the angle relative to the positive x-axis.
The connection between polar coordinates and Cartesian coordinates in a two-dimensional space assists in transforming the along and perpendicular components of a vector into magnitude and direction, or vice versa.
Example
If we had a vector with components Ax = 3 m east and Ay = 4 m north, and if the resulting vector A has a magnitude of 5 m directed north-east, we can illustrate that Ax + Ay equals vector A in a vector sense, but it is not a simple arithmetic addition of magnitudes.