- View vectors geometrically.
- Find magnitude and direction.
- Find the component form of a vector.
- Find the unit vector in the direction of v.
Vectors are essential tools for describing quantities that have both magnitude and direction, such as velocity, force, and displacement.
A delivery truck travels from a warehouse at point [latex]W(-3, 2)[/latex] to a store at point [latex]S(4, 5)[/latex], where coordinates represent city blocks. Find the position vector representing this displacement and graph both the original vector and position vector.
A drone flies from point [latex]A(-2, 1)[/latex] to point [latex]B(3, 5)[/latex], where coordinates are in meters. Find the position vector representing the drone’s displacement.
[latex]\mathbf{v} = \langle[/latex] [response area] [latex],[/latex] [response area] [latex]\rangle[/latex]
Correct answer: [latex]\langle 5, 4 \rangle[/latex]
Feedback for correct answer: Perfect! You correctly calculated [latex]3 - (-2) = 5[/latex] for the horizontal component and [latex]5 - 1 = 4[/latex] for the vertical component. The drone’s displacement is 5 meters east and 4 meters north.
Feedback for incorrect answer: Remember to subtract the initial point from the terminal point. The horizontal component is [latex]3 - (-2)[/latex] and the vertical component is [latex]5 - 1[/latex]. Be careful with the signs when subtracting negative numbers!
A search and rescue helicopter needs to fly from its base at point [latex]P(-8, 1)[/latex] to a hiker’s location at point [latex]Q(-2, -5)[/latex], where coordinates are in kilometers. Find the magnitude and direction of the displacement vector.
A sailboat travels from dock [latex]D(1, 4)[/latex] to buoy [latex]B(7, 12)[/latex], where coordinates are in nautical miles. Find the magnitude of the displacement vector (round to two decimal places).
[latex]|\mathbf{v}| =[/latex] [response area] nautical miles