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1.13 J: Vectors

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Question 45

A subterranean tunnel follows a linear path l l\,l connecting two access shafts. Relative to a fixed surveying origin OOO, where coordinates are measured in metres:

  • shaft A A\,A has position vector i+2j−3k\mathbf{i} + 2\mathbf{j} - 3\mathbf{k}i+2j−3k
  • shaft B B\,B has position vector 7i−j+0k7\mathbf{i} - \mathbf{j} + 0\mathbf{k}7i−j+0k
a.

(i) Find AB→\overrightarrow{AB}AB. (ii) Find a vector equation for the line l l\,l representing the tunnel path.

[3]
b.

A utility sensor is located at point C C\,C with position vector 5i+3j+2k5\mathbf{i} + 3\mathbf{j} + 2\mathbf{k}5i+3j+2k. A maintenance point P P\,P is located on lll.

Given that CP→\overrightarrow{CP}CP is perpendicular to lll:

Find the position vector of the point PPP.

[4]

1.13 J: Vectors Questions

  1. A Level
  2. /Maths
  3. /1.13 J: Vectors

Practise AQA A Level Maths 1.13 J: Vectors with exam-style questions for A Level Maths. 122 questions covering 1.13.1 Vectors in two and three dimensions, 1.13.2 Magnitude and direction of a vector, 1.13.3 Vector arithmetic, 1.13.4 Position vectors, and 1.13.5 Vectors to solve problems, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

Question bank