Given a Vector in Component Form, Find the Unit Vector

The video tutorial explains the concept of component form and unit vectors. It covers how to determine if a vector is a unit vector by checking its magnitude. The process of calculating the magnitude of a vector is demonstrated, followed by simplifying the unit vector and rationalizing denominators. The tutorial also discusses the relationship between unit vectors and the unit circle, emphasizing the importance of simplification in mathematical calculations.

What is a unit vector?

• A vector with a magnitude greater than 1

• A vector with a magnitude of 0

• A vector with a magnitude less than 1

• A vector with a magnitude of 1

How do you calculate the magnitude of a vector?

• By adding the components

• By multiplying the components

• By subtracting the components

• By squaring the components, adding them, and taking the square root

What is the magnitude of the vector (-2, 2)?

• 2

• 4

• 2√2

• 8

How do you convert a vector to its unit vector form?

• By adding the vector to its magnitude

• By dividing the vector by its magnitude

• By multiplying the vector by its magnitude

• By subtracting the vector from its magnitude

What is the simplified form of the unit vector for (-2, 2)?

• (-1/√2, 1/√2)

• (-1, 1)

• (-2, 2)

• (1, -1)

Why is rationalizing the denominator important in unit vector calculations?

• It has no effect on the vector

• It changes the direction of the vector

• It simplifies the vector for easier calculations

• It makes the vector longer

What is the significance of a unit vector lying on the unit circle?

• It has a magnitude less than 1

• It has a magnitude greater than 1

• It has a magnitude of 1

• It has a magnitude of 0