Question

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

Answer 1

Answer:

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.