Trigonometry Examples

$A = (- 4, 3)$ , $B = (1, 1)$

Step 1

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

$Q - P = (1 i + 1 j) - (- 4 i + 3 j)$

Step 2

Simplify each term.

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Step 2.1

Multiply $i$ by $1$ .

$i + 1 j - (- 4 i + 3 j)$

Step 2.2

Multiply $j$ by $1$ .

$i + j - (- 4 i + 3 j)$

Step 2.3

Apply the distributive property.

$i + j - (- 4 i) - (3 j)$

Step 2.4

Multiply $- 4$ by $- 1$ .

$i + j + 4 i - (3 j)$

Step 2.5

Multiply $3$ by $- 1$ .

$i + j + 4 i - 3 j$

Step 3

Simplify by adding terms.

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Step 3.1

Add $i$ and $4 i$ .

$j + 5 i - 3 j$

Step 3.2

Subtract $3 j$ from $j$ .

$- 2 j + 5 i$

Step 4