The vectors BD, OB, AC, and CO, where O is the point of intersection of the diagonals
| May 28, 2021 | education
The vectors BD, OB, AC, and CO, where O is the point of intersection of the diagonals of the parallelogram ABCD, expand into vectors a = AB and b = AD.
Vector ↑ VD = ↑ VA + ↑ AD = – ↑ AB + ↑ AD = – ↑ a + ↑ b = ↑ b – ↑ a.
Vector ↑ ОВ = ↑ DB / 2 = – ↑ ВD / 2 = – (↑ b – ↑ a) / 2 = (↑ a – ↑ b) / 2.
Vector ↑ АС = ↑ АD + ↑ DC = ↑ АD + ↑ AB = ↑ b + ↑ a.
Vector ↑ CO = ↑ CA / 2 = – ↑ AC / 2 = – (↑ a + ↑ b) / 2.
Answer: ↑ ВD = ↑ b – ↑ a, ↑ ОВ = (↑ a – ↑ b) / 2, ↑ AC = ↑ b + ↑ a, ↑ CO = – (↑ a + ↑ b) / 2.
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