Question
Sefine the points \( P(-9,5) \) and \( Q(-3,9) \). Carry out the following calculation. Express \( \overrightarrow{P Q} \) in the form \( a \mathbf{i}+\mathrm{bj} \). \( \overrightarrow{P Q}=(\square) \mathbf{i}+(\square) \mathbf{j} \) (Simplify your answers.)
Ask by John Powell. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
\overrightarrow{PQ} = 6\,\mathbf{i} + 4\,\mathbf{j}
\]
Solution
To find the vector \( \overrightarrow{PQ} \) in the form \( a\mathbf{i} + b\mathbf{j} \), follow these steps:
1. **Identify the coordinates of points \( P \) and \( Q \):**
- \( P(-9, 5) \)
- \( Q(-3, 9) \)
2. **Calculate the difference in the \( x \)-coordinates and the \( y \)-coordinates:**
- Difference in \( x \)-coordinates: \( x_Q - x_P = -3 - (-9) = 6 \)
- Difference in \( y \)-coordinates: \( y_Q - y_P = 9 - 5 = 4 \)
3. **Express the vector \( \overrightarrow{PQ} \) using the differences:**
\[
\overrightarrow{PQ} = 6\mathbf{i} + 4\mathbf{j}
\]
**Final Answer:**
\[
\overrightarrow{PQ} = 6\,\mathbf{i} + 4\,\mathbf{j}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To find the vector \( \overrightarrow{PQ} \), we can use the formula: \[ \overrightarrow{PQ} = Q - P \] Given the points \( P(-9, 5) \) and \( Q(-3, 9) \), we can calculate the components of the vector: 1. The x-component: \[ -3 - (-9) = -3 + 9 = 6 \] 2. The y-component: \[ 9 - 5 = 4 \] Putting it all together, we have: \[ \overrightarrow{PQ} = 6 \mathbf{i} + 4 \mathbf{j} \] So, the answer is: \[ \overrightarrow{PQ} = (6) \mathbf{i} + (4) \mathbf{j} \]
