When solving problems involving vectors, which option correctly represents the components used to resolve the vector into perpendicular directions?

When solving problems involving vectors, which option correctly represents the components used to resolve the vector into perpendicular directions?

• A. Magnitude
• B. Hypotenuse Components
• C. Diagonal Components
• D. X Y Components

Answer: (D)

Resolving vectors into perpendicular directions means breaking the vector into two parts along axes that are at right angles to each other—the x and y components. The magnitude is the length of the vector, not how it projects onto axes. The two components tell you how much of the vector lies along each axis, and you can use them to add vectors or find the resultant. If a vector has magnitude V and makes an angle θ with the x-axis, its horizontal (x) component is V cos θ and its vertical (y) component is V sin θ. That’s why describing the components as X Y Components best captures the idea of two separate, perpendicular projections. The other terms don’t represent standard directional components for resolving the vector.

Resolving vectors into perpendicular directions means breaking the vector into two parts along axes that are at right angles to each other—the x and y components. The magnitude is the length of the vector, not how it projects onto axes. The two components tell you how much of the vector lies along each axis, and you can use them to add vectors or find the resultant. If a vector has magnitude V and makes an angle θ with the x-axis, its horizontal (x) component is V cos θ and its vertical (y) component is V sin θ. That’s why describing the components as X Y Components best captures the idea of two separate, perpendicular projections. The other terms don’t represent standard directional components for resolving the vector.