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1.10 Vectors

1.10 Vectors

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Question 84

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

1.10 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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