Vectors in Two Dimensions | Cambridge O Level Additional Maths Topic Questions 2025

1

5 marks

The parallelogram $O A B C$ is such that $\vec{O A} = a$ and $\vec{O C} = c$ . The point $D$ lies on $O C$ such that $O D : D C$ = $1 : 2$ . The point $E$ lies on $A C$ such that $A E : E C$ = $2 : 1$ .

Show that $\vec{O B} = k \vec{D E}$ , where $k$ is an integer to be found.

How did you do?

Did this page help you?

1a

1 mark

Find the unit vector in the direction of $(\begin{matrix} 5 \\ - 12 \end{matrix})$ .

How did you do?

1b

3 marks

Given that $(\begin{matrix} 4 \\ 1 \end{matrix}) + k (\begin{matrix} - 2 \\ 3 \end{matrix}) = r (\begin{matrix} - 10 \\ 5 \end{matrix})$ , find the value of each of the constants $k$ and $r$ .

How did you do?

1c

4 marks

Relative to an origin $O$ , the points $A, B$ and $C$ have position vectors $p, 3 q - p and 9 q - 5 p$ respectively.

(i)

Find

\vec{A B}

in terms of

p

and

q

.

[1]

(ii)

Find

\vec{A C}

in terms of

p

and

q

.

[1]

(iii)

Explain why

A, B and C

all lie in a straight line.

[1]

(iv)

Find the ratio

A B : B C

.

[1]

How did you do?

Did this page help you?

1a

3 marks

A particle $P$ is initially at the point with position vector $(\begin{matrix} 30 \\ 10 \end{matrix})$ and moves with a constant speed of $10 {ms}^{- 1}$ in the same direction as $(\begin{matrix} - 4 \\ 3 \end{matrix})$ .

Find the position vector of $P$ after $t s$ .

How did you do?

1b

1 mark

As $P$ starts moving, a particle $Q$ starts to move such that its position vector after $t s$ is given by $(\begin{matrix} - 80 \\ 90 \end{matrix}) + t (\begin{matrix} 5 \\ 12 \end{matrix})$ .

Write down the speed of $Q$ .

How did you do?

1c

3 marks

Find the exact distance between $P$ and $Q$ when $t = 10$ , giving your answer in its simplest surd form.

How did you do?

Did this page help you?

	Download	View
Medium
Hard
Very Hard

Vectors in Two Dimensions (Cambridge O Level Additional Maths)

Topic Questions