Understanding Unit Vectors

The video explores the concept of unit vectors, which are vectors with a magnitude of one. It uses vector A as an example, explaining its direction and magnitude. The video demonstrates how to calculate the magnitude using the Pythagorean theorem and how to construct a unit vector by scaling down vector A. Finally, it verifies that the constructed unit vector has a magnitude of one, maintaining the same direction as vector A.

What is the defining characteristic of a unit vector?

• It has a magnitude less than one.

• It has a magnitude greater than one.

• It has a magnitude of one.

• It has a magnitude of zero.

In the example, what are the horizontal and vertical components of vector A?

• 3 and 5

• 4 and 3

• 5 and 4

• 3 and 4

How is the magnitude of vector A calculated?

• By adding the components

• By multiplying the components

• By subtracting the components

• By using the Pythagorean theorem

Why is vector A not considered a unit vector?

• It has a magnitude of ten.

• It has a magnitude of zero.

• It has a magnitude of five.

• It has a magnitude of one.

What operation is performed to convert vector A into a unit vector?

• Add the magnitude

• Multiply by the magnitude

• Subtract the magnitude

• Divide by the magnitude

What are the components of the unit vector U derived from vector A?

• 1/3 and 1/4

• 3/5 and 4/5

• 5/3 and 5/4

• 4/3 and 3/4

How can you verify that a vector is a unit vector?

• Check if its magnitude is greater than one.

• Check if its magnitude is one.

• Check if its magnitude is less than one.

• Check if its magnitude is zero.

What is the magnitude of the unit vector U?

• Zero

• One

• Five

• Ten

What mathematical operation is used to verify the magnitude of the unit vector?

• Addition

• Subtraction

• Multiplication

• Square root of the sum of squares

What is the significance of the 'hat' notation on a vector?

• It indicates a vector with a magnitude greater than one.

• It indicates a vector with a magnitude less than one.

• It indicates a vector with a magnitude of one.

• It indicates a vector with zero magnitude.