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1.10 Vectors

1.10 Vectors

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Question 96

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

1.10 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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