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.
