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Maths · Vectors and scalars, the addition of vectors

In a trapezium, the vector and then

In a trapezium, the vector \( \overline{B C}=\lambda \overline{A D} \) and \( \bar{P}=\overline{A C}+\overline{B D}=\mu \overline{A D}, \) then

  • A. \( \mu=\lambda+1 \)
  • B. \( \lambda=\mu+1 \)
  • C. \( \lambda+\mu=1 \)
  • D. \( \mu=2+\lambda \)

Step-by-step solution

Let AD = d, AB = a, BC = λd, CD = c. In trapezium, AB + BC + CD + DA = 0 gives a + c = (1-λ)d. Then AC = a + λd, BD = λd + c, so AC+BD = a+c+2λd = (1-λ)d+2λd = (1+λ)d = μd, hence μ = λ+1.
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