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Math

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PROBLEM

Find the vectors PQ\overrightarrow{P Q} and PR\overrightarrow{P R} for points P(2,1)P(-2,1), Q(5,3)Q(5,3), and R(x,y)R(x,y).

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 Q\overrightarrow{ Q}. The formula to find the vector from point to point Q is given byQ=Q\overrightarrow{ Q} = Q -

STEP 3

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

STEP 4

Perform the subtraction operation to find the vector Q\overrightarrow{ Q}.
Q=((2),31)=(7,2)\overrightarrow{ Q} = (-(-2),3-1) = (7,2)

STEP 5

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

STEP 6

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

SOLUTION

Perform the subtraction operation to find the vector R\overrightarrow{ R}.
R=(x(2),y1)=(x+2,y1)\overrightarrow{ R} = (x-(-2), y-1) = (x+2, y-1)So, the vectors Q\overrightarrow{ Q} and R\overrightarrow{ R} are (7,2) and (x+2, y-1) respectively.

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