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Vector

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

Unit Vectors

  • i hat
    • xx component
  • j hat
    • yy component

Adding Vectors

  • Resultant displacement vector (Dāƒ—R\vec{D}_R) is the sum of the vectors
    • A vector equation
    • Dāƒ—R=Dāƒ—1+Dāƒ—2\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
    • Dāƒ—Rā‰¤Dāƒ—1+Dāƒ—2\vec{D}_R \leq \vec{D}_1 + \vec{D}_2
  • Adding vectors is commutative
    • Vāƒ—1+Vāƒ—2=Vāƒ—2+Vāƒ—1\vec{V}_1 + \vec{V}_2 = \vec{V}_2 + \vec{V}_1

Aāƒ—+Bāƒ—=[AxAy]+[BxBy]=[Ax+BxAy+By]\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 (Dāƒ—1\vec{D}_1) to scale
  2. Draw second vector (Dāƒ—2\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 Dāƒ—1\vec{D}_1 to the tip of Dāƒ—2\vec{D}_2
    • This arrow represents the sum (resultant) of the two vectors
    • The length of the resultant represents its magnitude

Math Physics