ABCD-parallelogram. O-point of intersection of the diagonals. M-middle AB.
| June 20, 2021 | education
ABCD-parallelogram. O-point of intersection of the diagonals. M-middle AB. Vector DA = vector a, and vector DC = vector b. Find DB, DO, AC, DM.
Since the parallelogram has the same lengths of opposite sides, AB = DC, AD = BC.
Vector | ↑ DВ | = | ↑ DA | + | ↑ AB | = | ↑ DA | + | ↑ DC | = | ↑ a | + | ↑ b |.
Vector | ↑ DO | = | ↑ DВ | / 2 = (| ↑ a | + | ↑ b |) / 2.
Vector | ↑ AC | = | ↑ АD | + | ↑ DC | = – | ↑ DА | + | ↑ DC | = – | ↑ a | + | ↑ b | = | ↑ b | – | ↑ a |.
Vector | ↑ DM | = | ↑ DA | + | ↑ AM | = | ↑ DA | + | ↑ DC | / 2 = | ↑ a | + | ↑ b | / 2.
Answer: | ↑ DB | = | ↑ a | + | ↑ b |, | ↑ DO | = (| ↑ a | + | ↑ b |) / 2, | ↑ AC | = | ↑ b | – | ↑ a |, | ↑ DM | = | ↑ a | + | ↑ b | / 2.
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