Question

Why do we resolve a vector into x and y components?

A) To make it easier to draw.
B) To work with right angles.
C) To create a 3D vector.
D) To find the vector's scalar.

Answer 1

We resolve a vector into x and y components to simplify mathematical operations by using right angles, allowing us to add components along the same axis easily. Trigonometric functions help find each component, and the Pythagorean theorem determines the resultant vector's magnitude.

Step-by-step explanation:

The reason we resolve a vector into x and y components is to work with right angles, which makes mathematical operations simpler. By breaking a vector down into its horizontal (x-axis) and vertical (y-axis) components, we can easily use algebraic methods to add, subtract, or find the resultant of multiple vectors. Components on the same axis can be added like ordinary numbers because they are along the same line of action. This is often done by using trigonometric functions such as cosine and sine to determine the magnitude of the components along the chosen perpendicular axes.

To determine the components of a vector, you would typically use equations Ax = A cos θ and Ay = A sin θ, where θ is the angle the vector makes with the x-axis. Once the x and y components are known, we can apply the Pythagorean theorem to find the magnitude of the resultant vector when dealing with two-dimensional vector problems.