## 13 Problems with Their Each Solution to Practice Vector in Physics

### 1. Displacement vector

**Solution:**

### 2. Find the resultant magnitude of \overrightarrow{A}-\overrightarrow{B}

**Solution:**

### 3. Find angle and the magnitude of a resultant vector.

**Solution:**

### 4. Find the x-component and y-component of a vector and write it down using \hat{i} and \hat{j} notation

**Solution:**

### 5. Resultant of 3 vectors

- \overrightarrow{A}=4\hat{i}+5\hat{j}
- \overrightarrow{B}=9\hat{i}-7\hat{j}
- \overrightarrow{C}=-3\hat{i}+2\hat{j}

**Solution:**

### 6. Finding the angles of a vector

**Solution:**

### 7. Finding angles between 2 vectors which have same magnitude

**Solution:**

### 8. Resultant of 2 vectors in a square

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### 9. Calculate the resultant of 3 vectors which 2 of them are symmetric

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### 10. Resultant of Coulomb Forces

**Solution:**

Force | x-component | Y-Component |
---|---|---|

\overrightarrow{F_1} | \begin{aligned}F_{1x}=&F_1 \cos{30}\\=&8 \times \frac{1}{2}\sqrt{3}\\=&4\sqrt{3}\;\mu\text{N to the right} \end{aligned} | \begin{aligned}F_{1x}=&F_1 \cos{30}\\=&8 \times \frac{1}{2}\sqrt{3}\\=&4\sqrt{3}\;\mu\text{N to top} \end{aligned} |

\overrightarrow{F_2} | \begin{aligned}F_{2x}=&F_2 \sin{45}\\=&6 \times \frac{1}{2}\sqrt{2}\\=&3\sqrt{2} \;\mu \text{N to the left} \end{aligned} | \begin{aligned}F_{2y}=&F_2 \cos{45}\\=&6 \times \frac{1}{2}\sqrt{2}\\=&3\sqrt{2} \; \mu\text{N to top} \end{aligned} |

\overrightarrow{F_3} | \begin{aligned}F_{3x}=&F_3 \sin{30}\\=&10 \times \frac{1}{2}\\=&5 \; \mu\text{N to the left} \end{aligned} | \begin{aligned}F_{3y}=&F_3 \cos{30}\\=&10 \times \frac{1}{2}\sqrt{3}\\=&5\sqrt{2} \;\mu \text{N to bottom} \end{aligned} |

\overrightarrow{R} | \begin{aligned} R_x=&4\sqrt{3}-3\sqrt{2}-5\\=&2.314 \;\mu\text{N to the left}\end{aligned} | \begin{aligned}R_y=&4+3\sqrt{2}-5\sqrt{3}\\=&0.418\; \mu\text{N to bottom}\end{aligned} |

After we describe F_1, F_2, and F_3, then we add up these components to get the x and y component of the resultant vector. The calculations are in the last row of the table above. When adding components, be careful with the (-)(+) sign. Remember negative means the force is pointing to the left/bottom and positive means the force is pointing to the right/top.

### 11. Parabolic motion distance

**Solution:**

### 12. Finding the acceleration vector of an object

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### 13. Analyzing Newton's law using vectors

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