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Question 27

The points $A\,$ and $B\,$ have position vectors $(1−24)\begin{pmatrix} 1 \\ -2 \\ 4 \end{pmatrix}$ and $(3−52)\begin{pmatrix} 3 \\ -5 \\ 2 \end{pmatrix}$ respectively.

Find the exact length of $A B$ .

[2]

Find the position vector of the midpoint of $A B$ .

[2]

The points $P\,$ and $Q\,$ have position vectors $(421)\begin{pmatrix} 4 \\ 2 \\ 1 \end{pmatrix}$ and $(253)\begin{pmatrix} 2 \\ 5 \\ 3 \end{pmatrix}$ respectively. Show that $ABPQ\,$ is a parallelogram.

[3]

Markscheme

Vectors Questions

A Level
Maths
Vectors

109 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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Question 27

The points $A\,$ and $B\,$ have position vectors $(1−24)\begin{pmatrix} 1 \\ -2 \\ 4 \end{pmatrix}$ and $(3−52)\begin{pmatrix} 3 \\ -5 \\ 2 \end{pmatrix}$ respectively.

Find the exact length of $A B$ .

[2]

Find the position vector of the midpoint of $A B$ .

[2]

[3]

Markscheme

Vectors Questions

A Level
Maths
Vectors