Writing the unit vector given a vector in terms of i and j

The video tutorial explains how to find a unit vector, which has a magnitude of 1. It begins by discussing the concept of unit vectors and their properties. The tutorial then demonstrates how to calculate the magnitude of a vector using its components. Once the magnitude is determined, the video shows how to find the unit vector by dividing the original vector by its magnitude. Finally, it covers the preferred way to express the unit vector, emphasizing the importance of distributing the division across components.

What is the defining characteristic of a unit vector?

• It has a magnitude of 0.

• It has a magnitude of 1.

• It has a magnitude greater than 1.

• It has a magnitude less than 1.

How do you find the magnitude of a vector given its components?

• Divide the components by each other.

• Square each component, sum them, and take the square root.

• Multiply the components together.

• Add the components together.

What is the magnitude of a vector with components 2 and -4?

• 22

• 20

• 24

• 18

How do you convert a vector into a unit vector?

• Subtract the vector from its magnitude.

• Divide the vector by its magnitude.

• Add the vector to its magnitude.

• Multiply the vector by its magnitude.

What is the preferred way to express a unit vector from components 2 and -4?

• 2/sqrt(20)i - 4/sqrt(20)j

• 2i - 4j

• 4/sqrt(20)i + 2/sqrt(20)j

• 2i + 4j