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1.13 J: Vectors

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Question 51

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]

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

1.4 A: Proof
1.5 B: Algebra and functions
1.6 C: Coordinate geometry in the (x, y) plane
1.7 D: Sequences and series
1.8 E: Trigonometry
1.9 F: Exponentials and logarithms
1.10 G: Differentiation
1.11 H: Integration
1.12 I: Numerical methods (A-level only)
1.13 J: Vectors