Skip to content

Course home

1.11 Vectors

1.11 Vectors

EasyMediumHard
12345678910111213141516171819202122232425
Question 19

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

1.11 Vectors Questions

  1. A Level
  2. /Maths
  3. /1.11 Vectors

168 exam-style questions on OCR (MEI) A Level Maths 1.11 Vectors, covering 1.11.1 Language of vectors in two dimensions, 1.11.2 Add, subtract and scale vectors, 1.11.3 Magnitude and direction of a vector, 1.11.4 Position vectors, 1.11.5 Distance between points by position vectors, 1.11.6 Vectors to solve problems, 1.11.7 Language of vectors in three dimensions (A-level only), and 1.11 Vectors. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank