Further Mathematics (A2-Level)
Question 1 of 7
1. How confident are you in finding
a. the scalar product of two vectors?
Find the scalar product of
The formula for the scalar (or dot) product is
is the angle between the two vectors. It can also be found by multiplying the
components together and adding the result to the product of the
components (and the product of the
components for three dimensional vectors).
For this example then
What this might look like in the classroom
The main use of the scalar product is in finding the angle between two vectors. So re-arrange the formula:
In the above example this would give
Students could plot the two vectors on standard coordinate axes and estimate the angle before calculating it.
Students should also consider the implications in obtaining a zero scalar product from two non-zero vectors. This means that the two vectors are parallel (since a zero scalar product would mean the angle between the two vectors has to be zero also).
Taking this mathematics further
Students could also consider some of the properties of the scalar product. Is it commutatitve – so is a.b the same as b.a? What happens to the scalar product if one of the vectors is doubled?
Students will need to remember how to find the modulus of a vector – this should remind them of their previous study of Pythagoras’ theorem.
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