A vector is just a quantity that has both a size (how big) and a direction (which way). Think of it as an instruction like 'go 5 steps to the right'. A scalar, on the other hand, only has a size — like temperature or speed.
Vectors can be written as:
Column vectors: 3-2 means 3 right and 2 down (top number = horizontal, bottom = vertical)
Bold letters: a, b, or with an arrow: →AB
Adding vectors: add the corresponding components.
If a = 31 and b = 2-4, then a + b = 5-3.
Subtracting vectors: subtract the corresponding components.
a − b = 3-21-(-4) = 15.
Scalar multiplication: multiply each component.
3a = 3 × 31 = 93 — same direction, three times as long.
−a = -3-1 — same length, opposite direction.
Magnitude (length) of a vector: |v| = √(𝑥2 + y2)
For v = 34: |v| = √(9 + 16) = √25 = 5.