Final answer:
The subject poses a question on vector addition and components, where vectors are described by projecting onto axes in a coordinate system. Scalar components are found using trigonometric functions and the properties of vector algebra are used for vector addition and subtraction.
Step-by-step explanation:
The question deals with vector addition and vector components in a coordinate system. We know that vector addition is commutative, meaning A + B = B + A. Vectors in a plane can be expressed in terms of their x and y components, which are projections onto the axes defined by unit vectors î and ˇ.
To find the scalar components of vectors, we project them onto the respective axes. For example, to find the x-component of vector A, denoted as Ax, we use the cosine of the angle (θ) the vector makes with the horizontal axis: Ax = A*cos(θ). Similarly, the y-component Ay can be obtained using the sine of the same angle. If vector A is in a Cartesian coordinate system, it can be represented as A = Axî + Ayˇ, where Ax and Ay are the scalar multipliers of the unit vectors.
Using these concepts, one can perform algebraic operations on vectors, such as addition and subtraction, and calculate their magnitudes and directions. For instance, given two vectors B = −î − 4ˇ and A = −3î − 2ˇ, one can calculate A + B and its magnitude and direction angle, or A - B and its corresponding properties.