Vectors, direction and perpendicular components

Vectors, direction and perpendicular components

A vector has magnitude and direction; a scalar has magnitude only. Displacement, velocity, acceleration and force are vectors, so a complete answer must include a direction or a signed axis convention. In two dimensions, resolve a vector into perpendicular horizontal and vertical components before combining forces. If an angle is measured from the horizontal, use Fₓ = F cos θ and Fᵧ = F sin θ. Draw axes and arrows first; this prevents a sine/cosine swap and makes signs visible. The resultant is the single vector with the same effect as all component vectors together.

Work it through

A 10 N force acts 37° above the positive horizontal. Its horizontal component is 10 cos 37° ≈ 8.0 N and its vertical component is 10 sin 37° ≈ 6.0 N. Write +8.0 N horizontally and +6.0 N vertically if the chosen positive directions are right and up. A diagram and labels are evidence for the trigonometry.

Mastery target

Resolve a two-dimensional vector into signed perpendicular components, then use the components to describe a resultant with correct magnitude and direction.