1. What is the difference between a vector and a scalar?
2. Refer to Example 5 on p. 23. Assume that East is equivalent to the +x direction and North is equivalent to the +y direction.
   • The x- and y-components of D₁₂ are D_12X = 0 and D_12Y = 200 m.
     The x- and y-components of D₃₄ are D_34X = 20 m and D_34Y = 0.
     Find the x- and y-components of D₂₃.
   • Add the x-components of D₁₂, D₂₃, and D₃₄.
   • Add the y-components of D₁₂, D₂₃, and D₃₄.
   • Find the x- and y-components of D₁₄.
   • Say, "Aha."
   • Describe both graphically and mathematically what is meant by D₁₂ + D₂₃ + D₃₄ = D₁₄.
3. Vector A has components A_X = 5 and A_Y = 5. Find the magnitude and direction of A using
   
   

   A² = A_X² + A_Y² to find the magnitude and
   
   direction angle = Tan^-1 (A_Y / A_X) to find direction.

4. Vector B has components A_X = 8 and A_Y = 2. Find the magnitude and direction of B.
5. Find the x- and y-components of A + B.
6. Find the magnitude and direction of A + B.
7. Find the x- and y-components of B - A.
8. Find the magnitude and direction of B - A.
9. Find the magnitude and direction of 3A - B.
10. Vector C has magnitude 10 and direction 30^o above the +x axis.
    • Draw the vector to scale, including direction.
    • Measure the x- and y-components.
    • Calculate A_X = A cos (theta) and A_Y = A sin (theta).
    • Say, "Aha" again.

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