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5 marksVectors

CAPE Pure Mathematics Unit 1 · May/June 2017 · Paper 2 · Question 4(c)(i)

The vector equations of two lines, L₁ and L₂, are: L₁ = −i + j − 2k + α (−2i + j – 3k) L₂ = −2i + j − 4k + β (i − j + k)

Show that L₁ and L₂ intersect.

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Other parts of this question

  1. 4(a)(i)Express the equation of C₂ in the form (x – h)² + (y - k)² = k.[3 marks]
  2. 4(a)(ii)The equation of the line L₁ is x + 3y = 3. Determine whether L₁ is a tangent to the circle, C₁, in a (i) on page 16.[7 marks]
  3. 4(b)(i)Express the vector PQ in the form xi + yj + zk.[2 marks]
  4. 4(b)(ii)Determine the Cartesian equation of the plane which passes through the point Q and is perpendicular to PQ.[6 marks]
  5. 4(c)(ii)Hence, determine the coordinates of the point of intersection of the two lines.[2 marks]

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