Additional Mathematics – Vectors in two dimensions | e-Consult
Vectors in two dimensions (1 questions)
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- Vector v = QP = (1 − 7, 2 − (‑3)) = (‑6, 5).
- For parallelism, w = λ v. Thus (4, k) = λ(‑6, 5). Equating components:
- 4 = λ(‑6) ⇒ λ = ‑2/3.
- k = λ·5 = (‑2/3)·5 = ‑10/3, which is not an integer.
Therefore there is no integer k that makes w parallel to v.
- Since w = 2 × v, compute w:
2 × (‑6, 5) = (‑12, 10).
Vector PR = (‑12, 10) means R = P + (‑12, 10) = (1 ‑ 12, 2 + 10) = (‑11, 12).