W1.5 Sinning With Vectors
Probably the single biggest source of errors (and lost marks!) in student work comes through vector-abuse.
See if you can identify the most frequent types of errors… before we do.
Solution
Reveal

Solution
The Top Three Vector Sins
Equating a vector to a scalar
An equation like
WRONG! WRONG! is WRONG. The LHS is a vector; the ‘equals sign’ promises that there will be a vector on the RHS too.
Adding vector quantities as if they were scalars
You often need to consider the sum of two vectors. There is a tendency to think that
WRONG! WRONG! This is WRONG. The magnitude of the resultant of two vectors depends on their mutual orientation.
Multiplying vectors as if they were scalars There are two ways of multiplying vectors:
The scalar product:
The vector product:
But an equation involving
WRONG! WRONG! is WRONG. That particular combination of vectors is meaningless.