+x is to the right; +y is up

Vector **A** has a length of 3.76 cm and is at an angle of 34.5 degrees above the positive x-direction. Vector **B** has a length of 4.53 cm and is at an angle of 34.1 degrees above the negative x-direction.

What is the sum (resultant) of the two vectors?

The component method of vector addition is the standard way to add vectors. If **C** = **A** + **B**, then:
**C _{x}** =

Vector | x component | y component |
---|---|---|

A | A = +3.76 cos(34.5)_{x}A = +3.10 cm_{x} | A = +3.76 sin(34.5)_{y}A = +2.13 cm_{y} |

B | B = -4.53 cos(34.1)_{x}B = -3.75 cm_{x} | B = +4.53 sin(34.1)_{y}B = +2.54 cm_{y} |

C | C = _{x}A + _{x}B
_{x}C = -0.65 cm_{x} | C = _{y}A + _{y}B _{y}C = +4.67 cm_{y} |

State the resultant like this:

**C** = -0.65 cm + 4.67 cm

Or, glue the two components of **C** together to find the magnitude and direction of **C**.

C^{2} = C_{x}^{2} + C_{y}^{2} = 0.65^{2} + 4.67^{2}

C = 4.72 cm

tan(q) = 4.67 / 0.65

q = 82.1 degrees

So, the resultant vector has a magnitude of 4.72 cm and is 82.1 degrees above the -x direction.