Question

Determine the sum of the following vectors

a.5m, East + 3m, West

b.670 km, West + 550 km, South

c.2.5 cm, South + 3.09 cm, East

Answer 1

When the two vectors are added head-to-tail, the resultant is the hypotenuse of a right triangle. The resultant can be determined using the Pythagorean theorem.

Let R denotes the sum of the vectors

a.

$R^2 = 5^2 +3^2 \\ R^2 = 25+9 \\ R = 5.83 \;m$

b.

$R^2 = 670^2 + 550^2 \\ R^2 = 448900 + 302500 \\ R = 866.83 \;km$

c.

$R^2 = 2.5^2 + 3.09^2 \\ R^2 = 6.25 + 9.548 \\ R = 3.974 \; cm$