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

Studdy Solution

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 $\overrightarrow{ R}$ .
$\overrightarrow{ R} = R - = (x,y) - (-2,1)$

STEP 7

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.

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

Studdy Solution

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 $\overrightarrow{ R}$ .
$\overrightarrow{ R} = R - = (x,y) - (-2,1)$

STEP 7

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.

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

Studdy Solution

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 Qundefined\overrightarrow{ Q}Q​. The formula to find the vector from point to point Q is given byQundefined=Q−\overrightarrow{ Q} = Q -Q​=Q−

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

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

STEP 7

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

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.

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

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

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

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

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