Vector Components and Magnitude

The video tutorial explains how to find a unit vector in the direction of a given vector. It starts by identifying the vector's components and calculating its magnitude. The unit vector is then determined by dividing the original vector by its magnitude. The tutorial also covers rationalizing the components of the unit vector, providing both simplified and rationalized forms. The process is illustrated with a vector example, ensuring clarity in each step.

What is the initial point of the given vector?

• (0, 0)

• (1, 1)

• (-4, 2)

• (2, -4)

What is the x-component of the given vector?

• 4

• 0

• -4

• 2

How do you calculate the magnitude of a vector?

• Add the components

• Multiply the components

• Divide the components

• Square root of the sum of squares of components

What is the magnitude of the given vector?

• 2√5

• 5

• √20

• 10

How is the unit vector derived from the given vector?

• By multiplying the vector by its magnitude

• By adding 1 to each component

• By dividing the vector by its magnitude

• By subtracting 1 from each component

What is the simplified x-component of the unit vector?

• 2/√5

• -4/√5

• -2/√5

• 4/√5

What is the simplified y-component of the unit vector?

• 2/√5

• 1/√5

• -1/√5

• -2/√5

What is the process of rationalizing a denominator?

• Subtracting the numerator from the denominator

• Dividing the numerator by the denominator

• Multiplying by the square root of the denominator over itself

• Adding the numerator and denominator

What is the rationalized x-component of the unit vector?

• -4√5/5

• 4√5/5

• -2√5/5

• 2√5/5

What is the rationalized y-component of the unit vector?

• -2√5/5

• -√5/5

• 2√5/5

• √5/5