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1.10.7 Problem solving using vectors

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Question 17

The points $A\,$ and $B\,$ have position vectors $(−253)\begin{pmatrix} -2 \\ 5 \\ 3 \end{pmatrix}$ and $(21−1)\begin{pmatrix} 2 \\ 1 \\ -1 \end{pmatrix}$ respectively.

Find the exact length of $A B$ .

[2]

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

[1]

The points $P\,$ and $Q\,$ have position vectors $(7−5−2)\begin{pmatrix} 7 \\ -5 \\ -2 \end{pmatrix}$ and $(3−12)\begin{pmatrix} 3 \\ -1 \\ 2 \end{pmatrix}$ respectively. Show that $ABPQ\,$ is a parallelogram.

[3]

Markscheme

1.10.7 Problem solving using vectors Questions

A Level
Maths
1.10.7 Problem solving using vectors

65 exam-style questions on OCR A Level Maths 1.10.7 Problem solving using vectors. Each one has a worked solution and a mark scheme showing where the marks go.

1.10.7 Problem solving using vectors

Question bank

1.10.7 Problem solving using vectors

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Question 17

The points $A\,$ and $B\,$ have position vectors $(−253)\begin{pmatrix} -2 \\ 5 \\ 3 \end{pmatrix}$ and $(21−1)\begin{pmatrix} 2 \\ 1 \\ -1 \end{pmatrix}$ respectively.

Find the exact length of $A B$ .

[2]

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

[1]

[3]

Markscheme

1.10.7 Problem solving using vectors Questions

A Level
Maths
1.10.7 Problem solving using vectors

65 exam-style questions on OCR A Level Maths 1.10.7 Problem solving using vectors. Each one has a worked solution and a mark scheme showing where the marks go.