Learn to find the angle between two vectors

The video tutorial explains how to find the angle between two vectors using the cosine formula. It begins with an introduction to the concept and the use of the unit circle to understand vector components. The tutorial then covers the calculation of the dot product and magnitude of vectors, followed by the application of the cosine formula to determine the angle. The lesson concludes with a discussion on the restrictions of the cosine function and test instructions.

What is the cosine of π/4?

• 1

• 0

• -sqrt(2)/2

• sqrt(2)/2

Which point on the unit circle corresponds to 3π/2?

• (0, -1)

• (1, 0)

• (-1, 0)

• (0, 1)

How do you calculate the dot product of two vectors U and V?

• Divide the components of U by V

• Multiply corresponding components and add them

• Add the magnitudes of U and V

• Subtract the components of V from U

What is the magnitude of a vector with components (sqrt(2), sqrt(2))?

• 2sqrt(2)

• 2

• 1

• sqrt(2)

What is the cosine of the angle between two vectors if their dot product is -sqrt(2) and their magnitudes are both sqrt(2)?

• -sqrt(2)/2

• -1

• 1

• 0

Why is 4π/3 not a valid answer for the angle between the vectors?

• Cosine is negative in the fourth quadrant

• Cosine is positive in the third quadrant

• It is not in the second quadrant

• It is not in the first quadrant

In which quadrants is the cosine function restricted for inverse calculations?

• First and second

• First and fourth

• Third and fourth

• Second and third