Question

I had this class in college where the semester’s four exams weighed 10%, 15%, 25%, and 50%, respectively. The class average on each of the exams where 75%, 91%, 63%, 87%, respectively. Create two vectors in to represent the data. Calculate the dot product of your two vectors. What does the scalar value represent in terms of the class?

Answer 1

`v_(1).v_(2) = 0.804`

In terms of the class, the dot product represents the weighed class average.

Explanation:

The two vectors are:

-
`v_(1):` The weight of each of the semester's exams.

`v_(1) = (10%, 15%, 25%, 50%)`

In decimal:

`v_(1) = (0.10, 0.15, 0.25, 0.50)`

-
`v_(2):` The class average on each of the exams

In decimal:

`v_(2) = (0.75, 0.91, 0.63, 0.87)`

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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

------------------

So

`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`

`v_(1).v_(2) = 0.804`

In terms of the class, the dot product represents the weighed class average.