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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

Adding Vectors

  • 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
    • $\vec{D}_R \leq \vec{D}_1 + \vec{D}_2$
  • Adding vectors is commutative
    • $\vec{V}_1 + \vec{V}_2 = \vec{V}_2 + \vec{V}_1$

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

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

Math Physics