Questions: Define the points Q(-7,-8) and R(8,4). Carry out the following calculation. Express QR in the form a i+b j. QR= i j (Simplify your answers.)

Transcript text: Define the points $Q(-7,-8)$ and $R(8,4)$. Carry out the following calculation. Express $\overrightarrow{Q R}$ in the form $a i+b j$. $\overrightarrow{Q R}=$ $\square$ $\square$ $\mathbf{j}$ (Simplify your answers.)

Solution

Solution Steps

To express the vector $\overrightarrow{Q R}$ in the form $a i + b j$, we need to find the difference between the coordinates of points $R$ and $Q$. Specifically, we subtract the coordinates of $Q$ from the coordinates of $R$.

Step 1: Define the Points

We are given the points $ Q(-7, -8) $ and $ R(8, 4) $.

Step 2: Calculate the Components of the Vector

To find the vector $\overrightarrow{Q R}$, we subtract the coordinates of $ Q $ from the coordinates of $ R $: \[ a = 8 - (-7) = 8 + 7 = 15 \] \[ b = 4 - (-8) = 4 + 8 = 12 \]

Step 3: Express the Vector in the Form $ a i + b j $

The vector $\overrightarrow{Q R}$ can be expressed as: \[ \overrightarrow{Q R} = 15i + 12j \]