Vector Tools

Figure 3.1- Scalar increase

Figure 3.1: Vector AB is given.

[br]Circle C (center C) is not touching AB.[br]Using a compass and parallel line, vector CD is constructed equal to vector AB.

Figure 3.2 - Vector Sum

Figure 3.2: Vector AB and vector CD are given.

[br]Circle E (center E) is used to construct vector EF equal to vector AB (same length and same direction).[br]Circle F (center F) is used to construct vector FG equal to vector CD (same length and same direction).

Question 3.2

Given that EF = AB and FG = CD, what does EG represent?

Figure 3.3 - Scale vector by 1/n

[br]Extend line g from point B[br]Draw a circle around B with point D on g[br]Create the required n scalar value e.g. n =6 then 1/6AB requires 6DB[br][br]Drop a line from P_0 to A[br][br]Then Drop a parallel line from P_1, P_2, P_3, …, P_n to AB[br][br]This will cut AB into sections of 1/n[br][br][br]

Question 3.3.1

Using a compass, describe how you would construct point P₂ on line BP₁ given point P₁.

Question 3.3.2

Explain why the parallel lines from P₁, P₂, P₃, …, Pₙ divide AB into n equal sections.