1. The magnitude of a vector
The magnitude of a vector is its length. It is written with modulus signs: |a| is the magnitude of a and |overrightarrowAB| is the magnitude of overrightarrowAB.
The answer is a single number, not a vector. The vector beginpmatrixx yendpmatrix and its two components form a right-angled triangle, so Pythagoras gives the length.
The magnitude of (x,y) is the square root of (x² + y²).
|beginpmatrixx yendpmatrix| = √(x² + y²)
Examiner insight
“The magnitude of a vector notation was not always recognised and additions of column vectors or additions of components were often seen.” “A number of candidates were not familiar with the term ‘magnitude’ of a vector with some omitting the question and others adding the components.”
Worked example 12 marks
P is the point (3, 7) and Q is the point (7, 4). overrightarrowPQ = beginpmatrix4 -3endpmatrix. Work out |overrightarrowPQ|.
- 1
|overrightarrowPQ| = √(4² + (-3)²) [1]
- 2
= √(16 + 9) = √25 = 5 [1]