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Vector operations in one dimension

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Intros
Lessons
  1. Introduction to vector operations:
  2. What is the difference between adding scalars and vectors?
  3. Solving vector problems graphically
  4. Solving vector problems numerically
  5. Sign convention for vector problems
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Examples
Lessons
  1. Solve vector addition problems
    Solve the following vector additions graphically and numerically:

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

    ii. v⃗1+v⃗2=v⃗res\vec{v}_{1} + \vec{v}_{2} = \vec{v}_{res} if v⃗1=4.5m/s\vec{v}_{1} = 4.5 m/s [E], v⃗2=13.2m/s\vec{v}_{2} = 13.2 m/s [W]

    1. Solve vector subtraction problems
      Δd⃗1=1.2km\Delta \vec{d}_{1} = 1.2 km [N], Δd⃗2=0.8km\Delta \vec{d}_{2} = 0.8 km [N]. Solve the equation Δd⃗1−Δd⃗2=Δd⃗res\Delta \vec{d}_{1} - \Delta \vec{d}_{2} = \Delta \vec{d}_{res} graphically and numerically.
      1. Solve vector multiplication and division problems
        D⃗=12m/s \vec{D} = 12 m/s [W]. Solve the following graphically and numerically:

        i. 3D⃗=E⃗3\vec{D} = \vec{E}

        ii. -D⃗2=F⃗\frac{\vec{D}}{2} = \vec{F}

        1. 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 Δd⃗block\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 Δd⃗block\Delta \vec{d}_{block}

          iii. Find Tia's overall displacement.

          Topic Notes
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          In this lesson, we will learn:
          • How to add, subtract, multiply, and divide vectors
            • Graphically (with diagrams)
            • Numerically (with math)

          Notes:

          Just like scalars, vectors can be added, subtracted, multiplied, and divided:

          • When vectors are added, the vector diagram is drawn by tip-to-tail addition. To add A⃗\vec{A} and B⃗\vec{B}, draw the vector A⃗\vec{A}, then starting at the tip of A⃗\vec{A} draw B⃗\vec{B}. The tail of B⃗\vec{B} connects to the tip of A⃗\vec{A}.
          • Taking the negative of a vector "flips" the vector to point in the opposite direction, while keeping the same magnitude.
          • Multiplying or dividing a vector by a positive scalar changes the magnitude of the vector, while keeping the same direction.