A boat pushed east by its engine and north by the current does not travel along either arrow. It follows the diagonal. When two vectors meet at a right angle, that single diagonal, the resultant, comes straight from Pythagoras.
Two perpendicular vectors combine into a single resultant. Its magnitude is found from Pythagoras, R = √(x² + y²), and its direction from trigonometry, θ = tan⁻¹(y ÷ x). It can also be found by an accurate scale drawing.
Set the horizontal and vertical forces below to change the diagonal. Aim the resultant at the target ring to see how the single diagonal grows from the two perpendicular components, exactly as the parallelogram and tip-to-tail methods predict.
Four quick checks on combining perpendicular vectors. Each correct answer earns XP and lights this skill on your star map.
Two perpendicular forces combine into a single resultant that lies...
For two perpendicular components x and y, the magnitude of the resultant R is...
A 3 N force and a 4 N force act at right angles. The resultant is...
The parallelogram rule and the tip-to-tail triangle method give...
A 3 N force and a 4 N force at right angles do not give 7 N. Perpendicular vectors add by Pythagoras, not by simple addition, so the resultant is √(3² + 4²) = 5 N. Adding the magnitudes only works when the vectors point the same way; subtract them only when they point in exactly opposite directions.
A force of 6.0 N acts east and a force of 8.0 N acts north on the same object. Find the magnitude and direction of the resultant force.
Unlocks once the four checks above are done. Worth more XP, written in the style of Paper 2.
A force of 6.0 N acts east and a force of 8.0 N acts north on an object. The magnitude of the resultant is...
For that same resultant, the angle measured from the eastward force is...
A complete answer for a resultant force must give...
This skill is now lit gold on your star map. That completes the measurement topic.