# Vector operations in two dimensions

##### Intros
###### Lessons
1. Introduction to vector operations in two dimensions
##### Examples
###### Lessons
1. Perform tip-to-tail addition in two dimensions

A student arrives at school and from the entrance walks 20 m north to go to English. After, they walk 30 m east to physics class. What is their overall displacement? Answer with a vector diagram and a vector equation that describes the displacements.

Solve the following vector equations graphically:

i. $\Delta \vec{d}_{1} + \Delta \vec{d}_{2} = \Delta \vec{d}_{res}$

ii. $\vec{v}_{1} + \vec{v}_{2} = \vec{v}_{res}$

iii. $\vec{A} + \vec{B} + \vec{C} = \vec{D}$

1. Solve vector subtraction, multiplication, and division graphically

Solve the following vector equations graphically:

i. $\Delta \vec{d}_{1} - \Delta \vec{d}_{2} = \Delta \vec{d}_{res}$

ii. $2\vec{v}_{1} + 0.2 \vec{v}_{2} = \vec{v}_{res}$

iii. $\vec{A} - 2\vec{B} - \frac{\vec{C}}{2} = \vec{D}$

1. Write and draw the angles of vectors relative to compass directions

i. Write the vector using vector notation

ii. Draw the vector $\vec{C}$ = 2.5 m [40° S of E] on a set of compass axes.

1. Calculate two dimensional displacement with Trigonometry

A car drives at 13.8 m/s [W] for 115 s. It then turns left and travels south at 19.4 m/s for 135 s. Find the displacement of the car from its starting position.