chapter 2: vectors begin date: 1/22/2026 12:01:00 am due date: 2/8/2026 11:59:00 pm end date: 1/29/2027…
chapter 2: vectors begin date: 1/22/2026 12:01:00 am due date: 2/8/2026 11:59:00 pm end date: 1/29/2027 11:59:00 pm problem 6: (7% of assignment value) when two vectors are added together graphically, one can draw the vectors so that the tail of one vector touches the tip of the other. consider the three vectors shown in the figure labeled \\(\\vec{a}\\), \\(\\vec{b}\\), and \\(\\vec{c}\\). if the three vectors in the figure are added together \\(\\vec{a} + \\vec{b} + \\vec{c}\\) using the graphical method, in approximately what direction will the resultant be? \\(\\boldsymbol{\\cdot}\\) left \\(\\circ\\) up \\(\\circ\\) down \\(\\circ\\) right \\(\\circ\\) they add to zero, so there is no direction
Answer
Explanation:
Step1: Assign grid units to vectors
Let each grid square = 1 unit.
- $\vec{A}$: $\Delta x = 10$, $\Delta y = 3$
- $\vec{B}$: $\Delta x = -8$, $\Delta y = -2$
- $\vec{C}$: $\Delta x = -3$, $\Delta y = -7$
Step2: Sum x-components
$$\Delta x_{total} = 10 + (-8) + (-3) = -1$$
Step3: Sum y-components
$$\Delta y_{total} = 3 + (-2) + (-7) = -6$$
Step4: Analyze resultant direction
Total $\Delta x$ is negative (left), total $\Delta y$ is negative (down). The dominant component is $\Delta y_{total}$, so the resultant points mostly down, with a small leftward component.
Answer:
Down