Trigonometry Examples

$(- 1, 10)$ , $(5, 81)$

Step 1

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

$Q - P = (5 i + 81 j) - (- 1 i + 10 j)$

Step 2

Simplify each term.

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Step 2.1

Rewrite $- 1 i$ as $- i$ .

$5 i + 81 j - (- i + 10 j)$

Step 2.2

Apply the distributive property.

$5 i + 81 j - - i - (10 j)$

Step 2.3

Multiply $- 1$ by $- 1$ .

$5 i + 81 j + 1 i - (10 j)$

Step 2.4

Multiply $10$ by $- 1$ .

$5 i + 81 j + 1 i - 10 j$

Step 2.5

Multiply $i$ by $1$ .

$5 i + 81 j + i - 10 j$

Step 3

Simplify by adding terms.

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Step 3.1

Add $5 i$ and $i$ .

$81 j + 6 i - 10 j$

Step 3.2

Subtract $10 j$ from $81 j$ .

$71 j + 6 i$

Step 4