Foundation and Higher · vectors

Vectors:
add, multiply,
reverse.

every vector
is a journey

a vector tells you two things —

Size + direction

how far · which way

print: a · handwriting: a

step 1 of 4

Add: nose to tail

1. Follow a, then follow b.

2. Add the tops. Add the bottoms.

✓ a + b = (71) + (35) = (106)

step 2 of 4

Multiply by a number

1. 2a is a then a again: twice as long.

2. Multiply both numbers: 2 × (31) = (62)

✓ Multiples of a are parallel to a

step 3 of 4

Reverse and subtract

1. −b is b backwards: both signs flip.

2. a − b means follow a, then −b.

✓ a − b = (71) − (35) = (4−4)

step 4 of 4

Find a route

1. No arrow from A to B? Go round via O.

2. A to O is against the arrow: −a.
Then O to B is b.

✓ AB = −a + b = b − a

three moves —

a + b

nose to tail

2a

parallel, twice as long

−a

same length, reversed

Going against the arrow?
Make it negative.

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