Question

Let the vector v v have an initial point at ( 1 , − 7 ) (1,−7) and a terminal point at ( 3 , − 2 ) (3,−2). Determine the components of vector v . v.

Answer 1

Answer:  The vector is < 2, 5 >

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Explanation:

Label the initial point (1,-7) as point P and (3,-2) as point Q.

• The x coordinate of P is 1
• The x coordinate of Q is 3

This is a change of +2, meaning we move 2 units to the right.

Therefore, the x component of the vector is +2 or simply 2.

• The y coordinate of P is -7
• The y coordinate of Q is -2

This is a change of +5 when moving from P to Q. We have moved 5 units up. The y coordinate of the vector is +5 or simply 5.

Overall, the vector is < 2, 5 > which tells the reader "move 2 units to the right and 5 units up.

Refer to the diagram below.