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2 marksVectors

CAPE Pure Mathematics Unit 1 · May/June 2026 · Paper 2 · Question 4(b)(i)

Vectors a and b are such that a = 3i + 4j and b = -2i + j.

Calculate a · b.

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Other parts of this question

  1. 4(a)Determine the equation of the normal to the curve x = t², y = t + 1/t at the point on the curve where t = 2.[8 marks]
  2. 4(b)(ii)Hence, calculate the angle between the vectors a and b.[4 marks]
  3. 4(c)(i)Determine the displacement vector AB in terms of i, j and k.[2 marks]
  4. 4(c)(ii)Determine a unit vector parallel to AB in terms of i, j and k.[2 marks]
  5. 4(c)(iii)Determine the Cartesian equation of the line passing through A and B.[3 marks]
  6. 4(d)Determine the vector equation of the plane that passes through the point (1, -1, 2) and that is perpendicular to the vector 2i + 3j - k.[4 marks]

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