Vector operations in one dimension

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

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

    ii. v1+v2=vres\vec{v}_{1} + \vec{v}_{2} = \vec{v}_{res} if v1=4.5m/s\vec{v}_{1} = 4.5 m/s [E], v2=13.2m/s\vec{v}_{2} = 13.2 m/s [W]

    1. Solve vector subtraction problems
      Δd1=1.2km\Delta \vec{d}_{1} = 1.2 km [N], Δd2=0.8km\Delta \vec{d}_{2} = 0.8 km [N]. Solve the equation Δd1Δd2=Δdres\Delta \vec{d}_{1} - \Delta \vec{d}_{2} = \Delta \vec{d}_{res} graphically and numerically.
      1. Solve vector multiplication and division problems
        D=12m/s \vec{D} = 12 m/s [W]. Solve the following graphically and numerically:

        i. 3D=E3\vec{D} = \vec{E}

        ii. -D2=F\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 Δdblock\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 Δdblock\Delta \vec{d}_{block}

          iii. Find Tia's overall displacement.

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


          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 A\vec{A} and B\vec{B}, draw the vector A\vec{A}, then starting at the tip of A\vec{A} draw B\vec{B}. The tail of B\vec{B} connects to the tip of A\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.