Vector operations in one dimension

Lessons

• Introduction
  Introduction to vector operations:
  a)

  What is the difference between adding scalars and vectors?
  
  
  b)

  Solving vector problems graphically
  
  
  c)

  Solving vector problems numerically
  
  
  d)

  Sign convention for vector problems
  
  

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• 1.
  Solve vector addition problems
  Solve the following vector additions graphically and numerically:
  

  i. $\vec{A} + \vec{B} = \vec{C}$, if $\vec{A} = 10 m$ [E], $\vec{B} = 7 m$ [E].

  ii. $\vec{v}_{1} + \vec{v}_{2} = \vec{v}_{res}$ if $\vec{v}_{1} = 4.5 m/s$ [E], $\vec{v}_{2} = 13.2 m/s$ [W]

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• 2.
  Solve vector subtraction problems
  $\Delta \vec{d}_{1} = 1.2 km$ [N], $\Delta \vec{d}_{2} = 0.8 km$ [N]. Solve the equation $\Delta \vec{d}_{1} - \Delta \vec{d}_{2} = \Delta \vec{d}_{res}$ graphically and numerically.

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• 3.
  Solve vector multiplication and division problems
  $\vec{D} = 12 m/s$ [W]. Solve the following graphically and numerically:

  i. $3\vec{D} = \vec{E}$

  ii. -$\frac{\vec{D}}{2} = \vec{F}$

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• 4.
  Create Vector Equation and Diagram from Word Problem
  A city block is 50 m long. While doing errands, Tia walks 1 block east, then three fifths of a block west, then two blocks east.
  

  i. Write the displacement vector $\Delta \vec{d}_{block}$ that describes walking 1 block east.

  ii. Describe this situation with a vector equation and a vector diagram in terms of $\Delta \vec{d}_{block}$

  iii. Find Tia's overall displacement.

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