Answer:
[tex]v_{1}.v_{2} = 0.804[/tex]
In terms of the class, the dot product represents the weighed class average.
Step-by-step explanation:
The two vectors are:
-[tex]v_{1}:[/tex] The weight of each of the semester's exams.
[tex]v_{1} = (10%, 15%, 25%, 50%)[/tex]
In decimal:
[tex]v_{1} = (0.10, 0.15, 0.25, 0.50)[/tex]
-[tex]v_{2}:[/tex] The class average on each of the exams
In decimal:
[tex]v_{2} = (0.75, 0.91, 0.63, 0.87)[/tex]
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Dot product:
Suppose there are two vectors, u and v
u = (a,b,c)
v = (d,e,f)
There dot product between the vectors u and v is:
u.v = (a,b,c).(d,e,f) = ad + be + cf
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So
[tex]v_{1}.v_{2} = (0.10, 0.15, 0.25, 0.50).(0.75, 0.91, 0.63, 0.87) = 0.10*0.75 + 0.15*0.91 + 0.25*0.63 + 0.50*0.87 = 0.804[/tex]
[tex]v_{1}.v_{2} = 0.804[/tex]
In terms of the class, the dot product represents the weighed class average.
