Finding the Unit Vector of a Vector in Standard Form

The video tutorial explains the concept of unit vectors, which have a magnitude of 1, similar to the unit circle. It describes how to find a unit vector by dividing a given vector by its magnitude. An example is provided using a vector with components -2 and 5, demonstrating the calculation of its magnitude and the resulting unit vector. The tutorial verifies the unit vector's magnitude and concludes with a definition, emphasizing that dividing a vector by its magnitude always results in a unit vector.

What is the defining characteristic of a unit vector?

• It has a magnitude greater than 1.

• It has a magnitude of 1.

• It has a magnitude of 0.

• It has a magnitude less than 1.

Which theorem is used to find the magnitude of a vector?

• Fermat's Last theorem

• Fundamental theorem of calculus

• Binomial theorem

• Pythagorean theorem

What is the magnitude of the vector V = (-2, 5)?

• √13

• √29

• 7

• 5

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 should be the magnitude of a unit vector after conversion?

• 0

• 1

• Greater than 1

• Less than 1