Vectors: past paper questions

Where the questions come from

• Question 11Oct/Nov 2023, paper 31Structured10 marksHas a diagram

  In the diagram, $OABCDEFG$ is a cuboid in which $OA=3\text{ units}$, $OC=2\text{ units}$ and $OD=2\text{ units}$. Unit vectors $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$ are parallel to $OA$, $OD$ and $OC$ respectively. $M$ is the midpoint of $EF$.

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• Question 9Oct/Nov 2025, paper 33Structured9 marks

  The line $l_1$ passes through the point $(3,1,-6)$ and is parallel to the vector $2\mathbf{i}+\mathbf{j}+4\mathbf{k}$. The line $l_2$ passes through the point $(-1,3,-6)$ and is perpendicular to the vector $3\mathbf{i}-2\mathbf{j}+\mathbf{k}$.

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• Question 11Oct/Nov 2023, paper 33Structured9 marks

  The line $l$ has equation $\mathbf{r}=\mathbf{i}-2\mathbf{j}-3\mathbf{k}+\lambda (-\mathbf{i}+\mathbf{j}+2\mathbf{k})$. The points $A$ and $B$ have position vectors $-2\mathbf{i}+2\mathbf{j}-\mathbf{k}$ and $3\mathbf{i}-\mathbf{j}+\mathbf{k}$ respectively.

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• Question 8May/June 2025, paper 31Structured9 marks

  With respect to the origin $O$, the points $A$ and $B$ have position vectors $2\mathbf{i}+4\mathbf{k}$ and $5\mathbf{i}+\mathbf{j}+6\mathbf{k}$ respectively. The line $l_1$ passes through the points $A$ and $B$. Find a vector equation for the line $l_1$.

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• Question 11May/June 2023, paper 32Structured9 marks

  The points $A$ and $B$ have position vectors $\mathbf{i}+2\mathbf{j}-2\mathbf{k}$ and $2\mathbf{i}-\mathbf{j}+\mathbf{k}$ respectively. The line $l$ has equation $\mathbf{r}=\mathbf{i}-\mathbf{j}+3\mathbf{k}+\mu (2\mathbf{i}-3\mathbf{j}+4\mathbf{k})$.

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• Question 9May/June 2023, paper 33Structured10 marks

  The lines l and m have equations l : r = ai + 3j + bk + λ(ci - 2j + 4k), m : r = i + 2j + 3k + μ(2i - 3j + k). Relative to the origin O, the position vector of the point P is 4i + 7j - 2k.

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