Quelpr
5 marksVectors

CAPE Pure Mathematics Unit 1 · May/June 2011 · Paper 2 · Question 3(a)(i)

Let a = a₁i + a₂j and b = b₁i + b₂j with |a| = 13 and |b| = 10.

Find the value of (a+b)⋅(a-b).

The mark scheme is shown once you've answered.

Practise this question

Other parts of this question

  1. 3(a)(ii)If 2b - a = 11i, determine the possible values of a and b.[5 marks]
  2. 3(b)(i)Show that L passes through the centre of C.[2 marks]
  3. 3(b)(ii)If L intersects C at P and Q, determine the coordinates of P and Q.[3 marks]
  4. 3(b)(iii)Find the constants a, b and c such that x = b + a cos θ and y = c + a sin θ are parametric equations (in parameter θ) of C.[3 marks]
  5. 3(b)(iv)Another circle C₂, with the same radius as C, touches L at the centre of C. Find the possible equations of C₂.[7 marks]

More practice: the rest of this paper · more Vectors questions · all CAPE Pure Mathematics Unit 1 past papers