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.

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Solution

The Top Three Vector Sins

  1. Equating a vector to a scalar

    An equation like

    WRONG!
    $$\vec{p} = mv$$
    WRONG!

    is WRONG. The LHS is a vector; the ‘equals sign’ promises that there will be a vector on the RHS too.

  2. 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!
    $$\mid \vec{A} +\vec{B} \mid = A + B$$
    WRONG!

    This is WRONG. The magnitude of the resultant of two vectors depends on their mutual orientation.

  3. Multiplying vectors as if they were scalars There are two ways of multiplying vectors:

    The scalar product:

    $$\vec{A} \cdot \vec{B}$$

    The vector product:

    $$\vec{A} \times \vec{B}$$

    But an equation involving

    WRONG!
    $$\vec{A}\vec{B}$$
    WRONG!

    is WRONG. That particular combination of vectors is meaningless.