In parallelogram ABCD, point K lies on side BC, BK: KC = 3: 5. express the vector DK in terms of the vectors BA = a and BC = b.
| July 3, 2021 | education
Since ABCD is a parallelogram, then its opposite sides are equal, then BA = CD.
Let the length of the segment KC = 5 * X, then BK = 3 * X.
ВK = 3 * KС / 5.
BC = KC + BK.
KC + 3 * KC / 5 = BC.
KC = 5 * 8 / BC.
Then | ↑ KС | = 5 * b / 8.
Vector | ↑ DK | = | ↑ DС | + | ↑ СK | = – | ↑ BA | – | ↑ KC | = -a – (5 * b / 8).
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