Vectors: Notation, Addition and Scalar Multiples
Write vectors as columns or as bold letters, add and subtract them along a route, and multiply by a scalar to change length or reverse direction.
What a learner can do afterwards
- Add two column vectors and draw the result on a grid
- Write a route around a shape as a sum of named vectors
- Say what -2a does to the length and the direction of a
1 · Read
A column vector says how far right and how far up to go. To add, combine tops with tops and bottoms with bottoms. So (2, 3) plus (1, 4) is (3, 7). Draw the sum on a grid to check the arrow chain.
Routes add tip to tail. Walking vector a from A to B, then vector b from B to C, lands you at a plus b from A to C. Subtraction flips one arrow: a minus b means a plus a reversed b.
A scalar stretches or shrinks an arrow. The 2 in 2a doubles the length, and a minus sign spins it round. So minus 2a doubles the length of a and reverses its direction: a vector of length 5 becomes length 10.
Ask whether direction matters to spot a vector. Displacement and force point somewhere, so routes need vector addition. Plain arithmetic fits size-only quantities like mass.
Add columns top with top, chain routes tip to tail, and let scalars stretch or flip arrows.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.