How to find the angle between two vectors written as a linear combination

What is the formula used to find the cosine of the angle between two vectors?

• U dot V divided by the sum of magnitudes of U and V

• The product of U and V divided by their dot product

• U dot V divided by the product of magnitudes of U and V

• The sum of U and V divided by their dot product

Why might it be helpful to rewrite vectors in component form when calculating the dot product?

• It increases the magnitude of the vectors

• It changes the direction of the vectors

• It simplifies the calculation

• It makes the vectors longer

What is the dot product of vectors U and V if U1 = 2, U2 = 8, V1 = -2, and V2 = -1?

• 10

• -12

• 12

• -10

How is the magnitude of a vector calculated?

• By adding the components of the vector

• By subtracting the components of the vector

• By taking the square root of the sum of the squares of its components

• By multiplying the components of the vector

What is the approximate angle between the vectors U and V?

• 180 degrees

• 45 degrees

• 130.60 degrees

• 90 degrees