# Vector operations in two dimensions

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##### Intros

##### Examples

###### Lessons

**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 vector additions graphically**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. $\vec{A} + \vec{B} + \vec{C} = \vec{D}$

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

**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.

**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.