In which of the following situations does the scalar product of two vectors have the largest value? Group of answer choices

The angle between the two vectors is sixty degrees.

The angle between the two vectors is forty five degrees.

The angle between the two vectors is zero degrees.

The vectors are perpendicular to each other.

The angle between the two vectors is ninety degrees.

The angle between the two vectors is zero degrees.

Explanation:

In order to answer the question, you have to apply the definition of the scalar product of two vectors, which is:

AoB = |A||B|Cos (∅)

where A and B are vectors and ∅ is the angle between them.

The scalar product has the largest value if the value of Cos (∅) is maximum. By definition of cosine function, the maximum value is when cos (∅) = 1

You have to calculate the value of ∅. Applying ArcCos both sides:

ArcCos[Cos (∅) ] = ArcCos (1)

∅ = ArcCos (1) = 0 degrees.

So, the scalar product has the largest value when:

The angle between the two vectors is zero degrees.

Notice that you can also answer the question calculating the values of the scalar product for each choice:

|A||B| is the same value for all choices so the factor that determines the largest value of the product is Cos (∅). In other words, the largest value of Cos (∅) produces the largest value of the product.

If ∅=60, cos (60) = 0.5

If ∅=45, cos (45) = √2/2

If ∅=0, cos (0) = 1

If ∅=90, cos (90) = 0

The largest value of Cos∅ is given by ∅=0 degrees.