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12.3 Solving Geometric Problems

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Question 40

Relative to a fixed origin OOO,

  • the point AAA has position vector 2i+j+4k2\mathbf{i} + \mathbf{j} + 4\mathbf{k}2i+j+4k
  • the point BBB has position vector 5i−2j+k5\mathbf{i} - 2\mathbf{j} + \mathbf{k}5i−2j+k
  • the point CCC has position vector qi+3j+5kq\mathbf{i} + 3\mathbf{j} + 5\mathbf{k}qi+3j+5k

where qqq is a constant.

The line lll passes through AAA and BBB.

a.

Find a vector equation for the line lll.

[2]
b.

Given that AC⃗\vec{AC}AC is perpendicular to lll,

find the value of qqq.

[3]
c.

Hence find the area of triangle ABCABCABC, giving your answer as a surd in simplest form.

[4]

12.3 Solving Geometric Problems Questions

  1. A Level
  2. /Maths
  3. /12.3 Solving Geometric Problems

Practise Edexcel A Level Maths 12.3 Solving Geometric Problems with exam-style questions for A Level Maths. 55 questions, matched to the Edexcel A Level Maths (9MA0) 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