Add/subtract column vectors component by component
For add (or subtract) the tops and the bottoms separately. Scalar multiple multiplies BOTH components.
Magnitude is Pythagoras on the components
The length (magnitude) of is — the squares make signs irrelevant, so a negative component does not give a negative length.
Drawn from real examiner reports.
Finding the vector but then stopping
When asked for a length, students often work out the correct column vector (e.g. for ) and write that on the answer line, forgetting to go on and apply Pythagoras to get the magnitude.
Reversing the x and y components
Swapping the top and bottom of one vector before adding or subtracting scrambles the result.
Not knowing where to start with a vector path
Many simply added the two given vectors and assumed that was the answer, rather than building the required vector by following a route through the labelled points.
Read off the route, then compute
Write the required vector as a sum of journeys you know (e.g. ), substitute the columns, simplify, and only then take the magnitude if a length is asked for.
A vector means " across, up" (down/left are negative). Bold or both name vectors.
How do you add two column vectors?
Given and , work out as a column vector.
