Math Snap

STEP 1

Assumptions1. Points, Q, and R are in the same plane.
.(-,1), Q(5,3) are given points.
3. R(x, y) is an arbitrary point.

STEP 2

First, we need to find the vector $\overrightarrow{ Q}$. The formula to find the vector from point to point Q is given by$$\overrightarrow{ Q} = Q -$$

STEP 3

Now, plug in the given values for points and Q to calculate the vector $\overrightarrow{ Q}$.
$$\overrightarrow{ Q} = Q - = (5,3) - (-2,1)$$

STEP 4

Perform the subtraction operation to find the vector $\overrightarrow{ Q}$.
$$\overrightarrow{ Q} = (-(-2),3-1) = (7,2)$$

STEP 5

Now, we need to find the vector $\overrightarrow{ R}$. The formula to find the vector from point to point R is given by$$\overrightarrow{ R} = R -$$

STEP 6

Plug in the given values for points and R to calculate the vector $\overrightarrow{ R}$.
$$\overrightarrow{ R} = R - = (x,y) - (-2,1)$$

Perform the subtraction operation to find the vector $\overrightarrow{ R}$.
$$\overrightarrow{ R} = (x-(-2), y-1) = (x+2, y-1)$$So, the vectors $\overrightarrow{ Q}$ and $\overrightarrow{ R}$ are (7,2) and (x+2, y-1) respectively.