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Middle Years

13.03 Components of vectors

Worksheet
Components of vectors
1

Let G and H be the points G\left(11, 3\right)and H\left(12, - 2 \right).

a

Find the vector \overrightarrow{HG} in component form.

b

Find the exact length of the vector \overrightarrow{HG}.

2

Let P and Q be the points P\left(3, 3\right)and Q\left(6, 3\right).

a

Find the vector \overrightarrow{PQ} in component form.

b

Find the length of the vector \overrightarrow{PQ}.

3

Plot the vector with a magnitude of 17 and whose vertical component is greater than its horizontal component. Use the origin as the starting point of the vector.

4

A vector has a direction angle of 72 \degree and a vertical component of 22. Find x, its horizontal component, to the nearest whole number.

5

Consider the vector \mathbf{v} plotted on the graph:

a

Find the exact length of the horizontal component, a, of vector \mathbf{v}.

b

Find the exact length of the vertical component, b, of vector \mathbf{v}.

6

Consider the vector \mathbf{v} with magnitude 50 and direction angle 50 \degree.

a

Find the horizontal component of \mathbf{v}. Round your answer to the nearest tenth.

b

Find the vertical component of \mathbf{v}. Round your answer to the nearest tenth.

7

Consider the vector \mathbf{v} with magnitude 161 and direction angle 156.5 \degree.

a

Find the horizontal component of \mathbf{v}. Round your answer to the nearest tenth.

b

Find the vertical component of \mathbf{v}. Round your answer to the nearest tenth.

8

Write each of the following vectors in the form \left(a, b\right), for each of the following diagrams:

a
b
c
d
9

Consider the vector \begin{bmatrix} 8 \\ -3 \end{bmatrix}.

a

Find the horizontal component.

b

Find the vertical component.

10

Consider the vector with an initial point \left(2, 5\right) and a terminal point \left(4, 8\right). Find the x and y component.

11

Vector \mathbf{u}=\begin{bmatrix} a \\ b \end{bmatrix} is the directed segment from \left(4,-3\right) to \left(5,8\right). Find a and b.

12

Plot the vector with an x-component 5 and a y-component 9. Use the origin as the starting point for the vector.

13

Find the coordinates of the initial point of the following vectors:

a

A vector has a horizontal component 7 and a vertical component 4, and a terminal point \left(6, 3\right).

b

A horizontal vector has a horizontal component 6 and a terminal point \left(4, 3\right).

c

A vertical vector has a vertical component - 2 and a terminal point \left(7, 5\right).

14

A vector has a horizontal component 5 and a vertical component 7, and an initial point \left(2, 6\right). Find the coordinates of its terminal point.

Magnitude and direction
15

Find the angle \theta, to the nearest degree, for each of the plotted vector.

a
1
2
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8
x
1
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7
8
y
b
1
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9
x
1
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9
y
c
1
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9
x
1
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7
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9
y
d
1
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x
1
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9
y
16

Consider the vector \left( 2 \sqrt{3}, 2\right).

a

Find the magnitude of the vector.

b

Find the direction of the vector. Give your answer in degrees.

17

Express a force of 160 \text{ N} that is applied to the east as a vector.

18

Write the vector with a magnitude of 6 and a direction angle of 150 \degree as an ordered pair.

19

A bushwalker walks 12 \text{ km} west and then 35\text{ km} north in a day.

a

Find the magnitude of the bushwalker's resultant displacement.

b

Find the direction of the bushwalker's resultant displacement relative to due east. Round your answer to the nearest degree.

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