Precalculus Examples

$(2, - 3)$ , $(- 5, 7)$

Step 1

To find the position vector, subtract the initial point vector $P$ from the terminal point vector $Q$ .

$Q - P = (- 5 i + 7 j) - (2 i - 3 j)$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$- 5 i + 7 j - (2 i) - (- 3 j)$

Step 2.2

Multiply $2$ by $- 1$ .

$- 5 i + 7 j - 2 i - (- 3 j)$

Step 2.3

Multiply $- 3$ by $- 1$ .

$- 5 i + 7 j - 2 i + 3 j$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $2 i$ from $- 5 i$ .

$7 j - 7 i + 3 j$

Step 3.2

Add $7 j$ and $3 j$ .

$10 j - 7 i$

Step 4