Scalars and coplanar vectors

Repair the common break

Common misconception: Vector magnitudes can be combined without directions.

Correct model: Declare axes, resolve signed perpendicular components, combine like components, then recover magnitude and direction.

Worked transfer

For a 10 N force at 30° above +x, Fx = 10 cos 30° = 8.66 N and Fy = 10 sin 30° = 5.00 N. The components carry direction; they are not two extra forces.

Guided practice

Explain why “Vector magnitudes can be combined without directions.” fails. Then construct one example that correctly applies scalars and coplanar vectors.

Independent practice

Resolve a 24 N force directed 35° west of north into east–west and north–south components, including signs.

Return to the recorded repair plan when the explanation and application are secure enough to re-test.