Question

write the vector in component form.

Explanation:

Step1: Determine the change in x - coordinate

The initial point of the vector is \((0,0)\) and the terminal point is \((- 6,4)\). The change in \(x\) (denoted as \(\Delta x\)) is calculated as \(x_2 - x_1\), where \(x_1 = 0\) and \(x_2=-6\). So, \(\Delta x=-6 - 0=-6\).

Step2: Determine the change in y - coordinate

The change in \(y\) (denoted as \(\Delta y\)) is calculated as \(y_2 - y_1\), where \(y_1 = 0\) and \(y_2 = 4\). So, \(\Delta y=4 - 0 = 4\).

In component form, a vector \(\vec{v}\) is written as \(\langle\Delta x,\Delta y
angle\).

Answer:

\(\langle-6,4
angle\)