22.03 Components of vectors (Extended)

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

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

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.

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.

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

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

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

a

b

c

d

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

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.

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.

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

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

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.

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

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

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

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

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