Adding Vectors

To add vectors, place them tip to tail: start the second arrow where the first one ends. The resultant runs from the start of the first arrow to the tip of the last.

Tip to tail: R runs from the start of A to the end of B.

On a line, adding vectors is adding signed numbers. Two people pull a box, one with 40 N to the right and one with 25 N to the left. With right as positive, the total force is 40 + (-25) = 15 N to the right.

When the two vectors are perpendicular, the resultant is the hypotenuse of a right triangle, so Pythagoras gives its size:

R = √(A² + B²)

A hiker walks 4 km east, then 3 km north. Her displacement is √(4² + 3²) = 5 km from where she started, even though she walked 7 km.