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1.13.5 Vectors to solve problems

1.13.5 Vectors to solve 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]
Markscheme

1.13.5 Vectors to solve problems Questions

  1. A Level
  2. /Maths
  3. /1.13.5 Vectors to solve problems

67 exam-style questions on AQA A Level Maths 1.13.5 Vectors to solve problems. Each one has a worked solution and a mark scheme showing where the marks go.

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