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4 marksVectors

CAPE Pure Mathematics Unit 1 · May/June 2016 · Paper 2 · Question 4(b)(ii)

Let u = (1, -3, 2)ᵀ and v = (2, 1, 5)ᵀ be two position vectors in ℝ³.

Find cosθ where θ is the angle between u and v in ℝ³.

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Other parts of this question

  1. 4(a)(i)Given that sinθ = x, show that tanθ = x / √(1 - x²) where 0 < θ < π/2.[3 marks]
  2. 4(a)(ii)Hence, or otherwise, determine the Cartesian equation of the curve defined parametrically by y = tan(2t) and x = sin(t) for 0 < t < π/2.[5 marks]
  3. 4(b)(i)Calculate the lengths of u and v respectively.[3 marks]
  4. 4(c)Determine the Cartesian equation of the locus of P.[5 marks]
  5. 4(d)Determine the points of intersection of the circle C and the line L.[5 marks]

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