Question

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how do i work with vectors graphically?
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• solve vector problems using graphing

warm up
draw a vector map of the following story.
nevaeh and dayra decided to meet up for lunch. they started by walking 10 meters east on main st. at the corner, they made a left and continued walking for 8 meters until they came to a store. after shopping, they walked 5 meters east and 12 meters south before arriving at a bistro for lunch. after lunch, they walked 9 m west to the park to enjoy the sunshine.

Explanation:

Step1: Define directions

Let the positive x - axis be East, negative x - axis be West, positive y - axis be North and negative y - axis be South.

Step2: Analyze first part

The first vector $\vec{v}_1$ is $10$ m East, so in component form $\vec{v}_1=(10,0)$.

Step3: Analyze second part

A left - turn from East is North. The second vector $\vec{v}_2$ is $8$ m North, so $\vec{v}_2=(0,8)$.

Step4: Analyze third part

The third vector $\vec{v}_3$ is $5$ m East, so $\vec{v}_3=(5,0)$.

Step5: Analyze fourth part

The fourth vector $\vec{v}_4$ is $12$ m South, so $\vec{v}_4=(0, - 12)$.

Step6: Analyze fifth part

The fifth vector $\vec{v}_5$ is $9$ m West, so $\vec{v}_5=(-9,0)$.

Step7: Draw the vectors

Start from the origin $(0,0)$. Draw $\vec{v}_1$ as an arrow starting from the origin and ending at the point $(10,0)$. Then, starting from the tip of $\vec{v}_1$, draw $\vec{v}_2$ ending at the point $(10,8)$. From the tip of $\vec{v}_2$, draw $\vec{v}_3$ ending at the point $(15,8)$. From the tip of $\vec{v}_3$, draw $\vec{v}_4$ ending at the point $(15,-4)$. From the tip of $\vec{v}_4$, draw $\vec{v}_5$ ending at the point $(6,-4)$.

Answer:

Draw vectors as described above with starting point at the origin and each subsequent vector starting from the tip of the previous one. Vectors are $\vec{v}_1=(10,0)$, $\vec{v}_2=(0,8)$, $\vec{v}_3=(5,0)$, $\vec{v}_4=(0, - 12)$, $\vec{v}_5=(-9,0)$.