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1.10 Vectors

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Question 14

The points A A\,A and B B\,B have position vectors

a=2i+pj−k\mathbf{a} = 2\mathbf{i} + p\mathbf{j} - \mathbf{k}a=2i+pj−k and b=6i+3j+qk\mathbf{b} = 6\mathbf{i} + 3\mathbf{j} + q\mathbf{k}b=6i+3j+qk

where p p\,p and q q\,q are constants. The point C C\,C has position vector c=14i−3j+11k\mathbf{c} = 14\mathbf{i} - 3\mathbf{j} + 11\mathbf{k}c=14i−3j+11k.

AAA, B B\,B and C C\,C are collinear, with AB:BC=1:2AB : BC = 1 : 2AB:BC=1:2.

a.

Find the value of p p\,p and the value of qqq.

[5]
b.

Find the exact length of ACACAC.

[2]
Markscheme

1.10 Vectors Questions

  1. A Level
  2. /Maths
  3. /1.10 Vectors

197 exam-style questions on OCR A Level Maths 1.10 Vectors, covering 1.10.1 Vectors in two dimensions, 1.10.2 Vectors in three dimensions (A-level only), 1.10.3 Magnitude and direction of vectors, 1.10.4 Basic operations on vectors, 1.10.5 Position vectors, 1.10.6 Distance between points, 1.10.7 Problem solving using vectors, 1.10.8 Vectors in kinematics, and 1.10 Vectors. Each one has a worked solution and a mark scheme showing where the marks go.

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