A vector has size and direction. A column vector (3, −6) means 3 right and 6 down. To add vectors, add the top numbers and add the bottom numbers. To multiply by a number, multiply both parts: 3(−1, −6) = (−3, −18).
The vector from A to B, written AB, is B − A. With A = (−4, 2) and B = (−5, 1), AB = (−5 − (−4), 1 − 2) = (−1, −1). A negative vector points the opposite way: BA = −AB.
Worked example
a = (6, −4) and b = (−3, 1). Find a + 2b.
- 2b = (−6, 2).
- a + 2b = (6 + (−6), −4 + 2).
Answer:(0, −2)
Key words
- vector
- a quantity with size and direction
- column vector
- a vector written as (x, y) in a column
- scalar
- a number that multiplies a vector
Practise this
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Common Core-referenced: HSN-VM.A.2, HSN-VM.B.4