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4 marksVectors

CAPE Pure Mathematics Unit 1 · May/June 2024 · Paper 2 · Question 4(a)(i)

A plane, P, passes through the point (5, 1, -3) and is perpendicular to the vector n = 3i - 4j + 2k.

Show that the equation of the plane is 3x - 4y + 2z - 5 = 0.

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Other parts of this question

  1. 4(a)(ii)Calculate the angle, in radians, between P and the plane with equation 7x - 4y + 3z = 5.[6 marks]
  2. 4(b)(i)Determine the centre and radius of the circle.[5 marks]
  3. 4(b)(ii)Determine the equation of the tangent to the circle at the point (11, 4).[5 marks]
  4. 4(c)A point, Q, moves in the x-y plane such that it is equidistant from A(2, -5) and B(-2, 3). Determine the locus of Q.[5 marks]

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