a. Find the component form of $$ \vec{u} $$ and $$ \vec{v} $$. Round to the nearest hundredth. $$ \left.\begin{array}{ll} U \rightarrow & \begin{array}{l} \cos \left(55^{\circ}\right) \approx 0.5736 \ \ \sin \left(55^{\circ}\right) \approx 0.8192 \end{array} \ v_{x}=13 \cdot 0.5736 \approx 7.46 \ v_{y}=13 \cdot 0.8192 \approx 10.65 \end{array}\langle 7.46,10.65\rangle\begin{array}{l} \cos \left(165^{\circ}\right) \approx-0.9063 \ \sin \left(165^{\circ}\right) \approx 0.4226 \end{array} \quad \begin{array}{l} v_{x}=8 \cdot(-0.9063) \approx-7.25 \ v_{y}=8 \cdot 0.4226 \approx 3.38 \end{array}\right\rangle\langle-7.25,3.38\rangle $$ b. Find the component form of the resultant vector, $$ \vec{u}+\vec{v} $$. Round to the nearest hundredth.

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a. Find the component form of $$ \vec{u} $$ and $$ \vec{v} $$. Round to the nearest hundredth. $$ \left.\begin{array}{ll} U \rightarrow & \begin{array}{l} \cos \left(55^{\circ}\right) \approx 0.5736 \ \ \sin \left(55^{\circ}\right) \approx 0.8192 \end{array} \ v_{x}=13 \cdot 0.5736 \approx 7.46 \ v_{y}=13 \cdot 0.8192 \approx 10.65 \end{array}>\langle 7.46,10.65\rangle>\begin{array}{l} \cos \left(165^{\circ}\right) \approx-0.9063 \ \sin \left(165^{\circ}\right) \approx 0.4226 \end{array} \quad \begin{array}{l} v_{x}=8 \cdot(-0.9063) \approx-7.25 \ v_{y}=8 \cdot 0.4226 \approx 3.38 \end{array}\right\rangle\langle-7.25,3.38\rangle $$ b. Find the component form of the resultant vector, $$ \vec{u}+\vec{v} $$. Round to the nearest hundredth.

UpStudy AI · Accepted Answer

**b. Find the component form of the resultant vector, $$ \vec{u} + \vec{v} $$.**

From part **a**, we have the component forms of the vectors:

$$
\vec{u} = \langle 7.46, 10.65 \rangle
$$
$$
\vec{v} = \langle -7.25, 3.38 \rangle
$$

To find the resultant vector $$ \vec{u} + \vec{v} $$, we add the corresponding components of $$ \vec{u} $$ and $$ \vec{v} $$:

$$
\vec{u} + \vec{v} = \langle 7.46 + (-7.25),\ 10.65 + 3.38 \rangle
$$

$$
\vec{u} + \vec{v} = \langle 0.21,\ 14.03 \rangle
$$

**Therefore, the component form of the resultant vector is:**

$$
\vec{u} + \vec{v} = \langle 0.21,\ 14.03 \rangle
$$
The resultant vector $$ \vec{u} + \vec{v} $$ is $$ \langle 0.21, 14.03 \rangle $$.

a. Find the component form of and . Round to the nearest hundredth.

b. Find the component form of the resultant vector, . Round to the nearest hundredth.

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a. Find the component form of and . Round to the nearest hundredth. b. Find the component form of the resultant vector, . Round to the nearest hundredth.