Question

Give the component form of the following vectors shown.

NOTE: Answer must be typed in using the following format -- including the parentheses: (#,#)

Answer 1

The component form of the vector, starting at (-1, -1) and ending at (3, 4), is (4, 5). This indicates a displacement of 4 units horizontally and 5 units vertically in the coordinate system.

The component form of a vector is determined by subtracting the initial point from the terminal point. In this case, the vector starts at (-1, -1) and ends at (3, 4).

To find the component form, subtract the corresponding coordinates: (3 - (-1), 4 - (-1)), resulting in the component form (4, 5).

`\[\text{Component form} = (\text{terminal point} - \text{initial point}) = (3 - (-1), 4 - (-1)) = (4, 5)\]`

This means the vector moves 4 units in the horizontal (x) direction and 5 units in the vertical (y) direction.

The component form succinctly represents the vector's displacement, providing insight into its magnitude and direction along the x and y axes in a coordinate system.