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EXAMPLE 1Finding a Position Vector

Find the unique position vector v of a vector whose initial point is P1 and whose terminal point is P2.

  1. (a) P1=(−1,2),P2=(4,6)
  2. (b) P1=(3,4,2),P2=(7,−8,5)

Solution To find v, subtract corresponding components.

  1. (a) Then v=⟨4−(−1),6−2⟩=⟨5,4⟩, as shown in Figure 27.
  2. (b) Here, v=⟨7−3,−8−4,5−2⟩=⟨4,−12,3⟩