3 mistakes learners make with vector arithmetic, each one named and explained.
Add or subtract the components separately, and keep the signs.
The two components are treated differently, usually where one of them is negative.
A negative component makes adding look like subtracting, so the operation flips halfway.
Question. (3, -2) + (1, 4)
A common answer. (4, -6)
The answer. (4, 2)
Why. Minus 2 plus 4 is 2, because adding to a negative number moves it upwards.
Do each component as its own small sum, written out. Negative numbers cause this every time.
Corresponding components are multiplied together rather than added.
Two lists of numbers side by side invites combining them however seems natural.
Question. (3, -2) + (1, 4)
A common answer. (3, -8)
The answer. (4, 2)
Why. Adding vectors means adding each pair of components.
The operation in the question applies to each component separately, unchanged.
2p is worked out by adding 2 to each component.
Both operations use the same two symbols side by side and neither is written out in words.
Question. p = (5, -3), find 2p
A common answer. (7, -1)
The answer. (10, -6)
Why. 2p means two of the vector p, which is p added to itself.
Read 2p as two lots of p. Two lots is always a multiplication.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.