Skip to content

Course home

1.11 Vectors

1.11 Vectors

EasyMediumHard
12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970
Question 70

A subterranean survey records the following data relative to a fixed origin OOO:

  • The path of a straight tunnel lll starts at the point AAA with position vector i+4j−2k\mathbf{i} + 4\mathbf{j} - 2\mathbf{k}i+4j−2k
  • The tunnel passes through the point BBB with position vector 3i+2j+2k3\mathbf{i} + 2\mathbf{j} + 2\mathbf{k}3i+2j+2k
  • A significant mineral deposit is located at the point PPP with position vector −4i+j+2k-4\mathbf{i} + \mathbf{j} + 2\mathbf{k}−4i+j+2k

Units are measured in decametres.

a.

Find a vector equation for the line lll representing the tunnel.

[2]
b.

A side-shaft is planned to run from PPP to a point CCC on lll such that PCPCPC is perpendicular to lll. Determine the coordinates of CCC.

[4]
c.

A pressure sensor is placed at the point P′P'P′, where P′P'P′ is the reflection of PPP in the line lll. Find the coordinates of P′P'P′.

[2]
d.

Hence, calculate the distance between the mineral deposit and the sensor, ∣PP′→∣|\overrightarrow{PP'}|∣PP′∣, giving your answer as a simplified surd.

[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