# Vector

• Quantities with
• Direction
• Angle
• Can be larger than 90˚
• Magnitude
• $|\vec{V}|$
• Always positive
• A minus sign tells us about its direction
• Vectors have components not coordinates

## Unit Vectors

• i hat
• $x$ component
• j hat
• $y$ component

• Resultant displacement vector ($\vec{D}_R$) is the sum of the vectors
• A vector equation
• $\vec{D}_R = \vec{D}_1 + \vec{D}_2$
• The resultant vector is not equal to the sum of the magnitudes of two separate vectors, it is smaller than their sum
• $\vec{D}_R \leq \vec{D}_1 + \vec{D}_2$
• $\vec{V}_1 + \vec{V}_2 = \vec{V}_2 + \vec{V}_1$

$\vec{A} + \vec{B} = \begin{bmatrix}Ax\Ay\end{bmatrix} + \begin{bmatrix}Bx\By\end{bmatrix} = \begin{bmatrix}Ax + Bx\Ay + By\end{bmatrix}$

### Tail-to-Tip Method

1. Draw on vector ($\vec{D}_1$) to scale
2. Draw second vector ($\vec{D}_2$) to scale, placing its tail at the tip of the first vector
• Make sure its direction is correct!
3. Draw an arrow from the tail of $\vec{D}_1$ to the tip of $\vec{D}_2$
• This arrow represents the sum (resultant) of the two vectors
• The length of the resultant represents its magnitude