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Question 69

Relative to a fixed origin OOO, the point A A\,A has position vector (3i−3j+4k)(3\mathbf{i} - 3\mathbf{j} + 4\mathbf{k})(3i−3j+4k), the point B B\,B has position vector (5i−7j−k)(5\mathbf{i} - 7\mathbf{j} - \mathbf{k})(5i−7j−k), and the point C C\,C has position vector (ai−2j+2k)(a\mathbf{i} - 2\mathbf{j} + 2\mathbf{k})(ai−2j+2k), where a a\,a is a constant and a>0a > 0a>0. D D\,D is the point such that AB⃗=BD⃗\vec{AB} = \vec{BD}AB=BD

a.

Find the position vector of DDD.

[2]
b.

Given that ∣AC⃗∣=4|\vec{AC}| = 4∣AC∣=4, find the value of aaa.

[3]
Markscheme

Vectors Questions

  1. A Level
  2. /Maths
  3. /Vectors

309 exam-style questions on Edexcel A Level Maths Vectors, covering 12.1 3D Coordinates, 12.2 Vectors in 3D, 12.3 Solving Geometric Problems, and 12.4 Application to Mechanics. Each one has a worked solution and a mark scheme showing where the marks go.

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