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Question 1

HLPaper 1

Given vectors $\vec{a}=\left[\begin{array}{c}4 \\ -2\end{array}\right]$ and $\vec{b}=\left[\begin{array}{l}1 \\ 3\end{array}\right]$ , find the vector $\vec{r}$ such that $\vec{r}$ is perpendicular to both $\vec{a}$ and $\vec{b}-\vec{a}$ .

1.

Given vectors $\vec{a}=\left[\begin{array}{c}4 \\ -2\end{array}\right]$ and $\vec{b}=\left[\begin{array}{l}1 \\ 3\end{array}\right]$ , find the vector $\vec{r}$ such that $\vec{r}$ is perpendicular to both $\vec{a}$ and $\vec{b}-\vec{a}$ .

[5]

Question 2

HLPaper 1

Find the unit vector in the direction of $\vec{b}=\left[\begin{array}{l}6 \\ 8\end{array}\right]$ .

1.

Find the unit vector in the direction of $\vec{b}=\left[\begin{array}{l}6 \\ 8\end{array}\right]$ .

[2]

Question 3

HLPaper 1

Let $\vec{u}=\left[\begin{array}{c}2 \\ -1\end{array}\right]$ and $\vec{v}=\left[\begin{array}{c}-3 \\ 4\end{array}\right]$ .

1.

Find $\vec{u}+\vec{v}$ .

[2]

Question 4

HLPaper 1

A triangle has vertices $A(1,2), B(4,6)$ , and $C(k, 10)$ .

1.

Given that $\overrightarrow{A B}$ and $\overrightarrow{A C}$ are perpendicular, find the value of $k$ .

[5]

Question 5

HLPaper 1

The position vectors of points $A, B$ , and $C$ relative to the origin $O$ are:

\overrightarrow{O A}=\left[\begin{array}{l} 1 \\ 3 \end{array}\right], \quad \overrightarrow{O B}=\left[\begin{array}{l} 4 \\ 5 \end{array}\right], \quad \overrightarrow{O C}=\left[\begin{array}{l} 7 \\ k \end{array}\right]

1.

Given that $\overrightarrow{A B}$ and $\overrightarrow{A C}$ are parallel, find the value of $k$ .

[4]

Question 6

HLPaper 1

Let $\vec{a}=\left[\begin{array}{c}2 \\ -1\end{array}\right]$ and $\vec{b}=\left[\begin{array}{c}4 \\ -2\end{array}\right]$ .

1.

Show that $\vec{a}$ and $\vec{b}$ are parallel.

[2]

Question 7

HLPaper 1

Write down the magnitude of the vector $\vec{a}=\left[\begin{array}{l}3 \\ 4\end{array}\right]$ .

1.

Write down the magnitude of the vector $\vec{a}=\left[\begin{array}{l}3 \\ 4\end{array}\right]$ .

[2]

Question 8

HLPaper 1

If $\vec{a}=\left[\begin{array}{l}5 \\ 2\end{array}\right]$ , find the vector $-2 \vec{a}$ .

1.

If $\vec{a}=\left[\begin{array}{l}5 \\ 2\end{array}\right]$ , find the vector $-2 \vec{a}$ .

[2]

Question 9

HLPaper 1

Let $\vec{a}=\left[\begin{array}{l}1 \\ 2\end{array}\right]$ and $\vec{b}=\left[\begin{array}{c}-3 \\ 5\end{array}\right]$ .

1.

Find the magnitude of $\vec{a}+\vec{b}$ .

[3]

Question 10

HLPaper 1

Given points $P(1,2), Q(4,5)$ , and $R(7,8)$ , determine whether the points are collinear using vectors.

1.

Given points $P(1,2), Q(4,5)$ , and $R(7,8)$ , determine whether the points are collinear using vectors.

[3]

AHL 3.10—Vector definitions Questionbank