If vector A has components described as Ax = Acosθ and Ay = Asinθ, what choice best describes vector A?

If vector A has components described as Ax = Acosθ and Ay = Asinθ, what choice best describes vector A?

• A. A vector in standard position
• B. A unit vector
• C. A vector in component form
• D. A scalar quantity

Answer: (C)

The correct description of vector A, having components defined as Ax = Acosθ and Ay = Asinθ, is that it is a vector in component form. In component form, a vector is expressed in terms of its horizontal and vertical components, which are calculated using trigonometric functions based on the vector's magnitude and the angle θ it makes with the horizontal axis. This representation allows for clear identification of the vector's direction and magnitude by breaking it down into its individual x (horizontal) and y (vertical) components. The definitions given use cosine for the x-component and sine for the y-component, which is the standard method of converting from magnitude and angle to component form in a Cartesian coordinate system. While a vector in standard position is one that starts from the origin of the coordinate system, a unit vector has a magnitude of one and is typically expressed with a similar component breakdown but normalized. A scalar quantity is simply a magnitude without any direction, which does not apply to vector A in this case since it clearly has direction indicated through its trigonometric components. Hence, describing vector A as a vector in component form accurately reflects its mathematical definition.

The correct description of vector A, having components defined as Ax = Acosθ and Ay = Asinθ, is that it is a vector in component form. In component form, a vector is expressed in terms of its horizontal and vertical components, which are calculated using trigonometric functions based on the vector's magnitude and the angle θ it makes with the horizontal axis.

This representation allows for clear identification of the vector's direction and magnitude by breaking it down into its individual x (horizontal) and y (vertical) components. The definitions given use cosine for the x-component and sine for the y-component, which is the standard method of converting from magnitude and angle to component form in a Cartesian coordinate system.

While a vector in standard position is one that starts from the origin of the coordinate system, a unit vector has a magnitude of one and is typically expressed with a similar component breakdown but normalized. A scalar quantity is simply a magnitude without any direction, which does not apply to vector A in this case since it clearly has direction indicated through its trigonometric components. Hence, describing vector A as a vector in component form accurately reflects its mathematical definition.