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Vector Subtraction: PQ − PR from Three Given Points

Subtract directed vectors PQ and PR from the given coordinates and express the result as ⟨4,−2⟩ and 4i − 2j.

Question

With P=(−1,3)P=(-1,3), Q=(1,5)Q=(1,5), and R=(−3,7)R=(-3,7), calculate PQ→−PR→\overrightarrow{PQ}-\overrightarrow{PR}. Give the result (a) as components and (b) as a linear combination of the standard unit vectors i\mathbf i and j\mathbf j.

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Evidence boundary

The coordinates, vector order, and two requested answer forms come from OpenStax Calculus Volume 3, Section 2.1, Exercise 6 and its shared instructions. No coordinates are inferred from a drawing. The result is independently checked as the directed vector from R to Q.