Precalculus Examples

(1, 2)

$(1, 2)$ ,

(- 5, - 7)

$(- 5, - 7)$

Step 1

To find the position vector, subtract the initial point vector

P

$P$ from the terminal point vector

Q

$Q$ .

Q - P = (- 5 i - 7 j) - (1 i + 2 j)

$Q - P = (- 5 i - 7 j) - (1 i + 2 j)$

Step 2

Simplify each term.

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Step 2.1

Multiply

i

$i$ by

1

$1$ .

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

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

Step 2.2

Apply the distributive property.

- 5 i - 7 j - i - (2 j)

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

Step 2.3

Multiply

2

$2$ by

- 1

$- 1$ .

- 5 i - 7 j - i - 2 j

$- 5 i - 7 j - i - 2 j$

- 5 i - 7 j - i - 2 j

$- 5 i - 7 j - i - 2 j$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract

i

$i$ from

- 5 i

$- 5 i$ .

- 7 j - 6 i - 2 j

$- 7 j - 6 i - 2 j$

Step 3.2

Subtract

2 j

$2 j$ from

- 7 j

$- 7 j$ .

- 9 j - 6 i

$- 9 j - 6 i$

- 9 j - 6 i

$- 9 j - 6 i$

Step 4

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