In parallelogram ABCD, point O-is the intersection point of its diagonals. express the vector AO in terms of the vector CD, DA.
| April 3, 2021 | education
Vector ↑ AC = ↑ AB + ↑ VO.
Since the opposite sides of the parallelogram are equal and parallel, the vector ↑ AB = – ↑ CD.
Vector ↑ BO = ↑ BD / 2.
Vector ↑ BD = ↑ DA + ↑ AB = ↑ DA – ↑ CD.
Then the vector ↑ BO = (↑ DА – ↑ СD) / 2.
Vector ↑ AO = – ↑ СD + (↑ DА – ↑ СD) / 2 = ↑ DA – 3 * ↑ СD / 2.
Answer: ↑ AO = ↑ DA – 3 * ↑ CD / 2.
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