Unit Vectors and Their Applications

This video tutorial covers unit vectors, focusing on determining unit vectors in the same direction as a given vector and vectors intersecting the unit circle. It explains the concept of unit vectors, particularly the i and j vectors, and how any vector can be expressed as a linear combination of these. The process of normalizing a vector to find a unit vector is detailed, along with examples. The video also discusses the unit circle's role in understanding vectors and provides graphical representations to aid comprehension.

What is the magnitude of a unit vector?

• One

• Undefined

• Zero

• Two

Which of the following represents the vector i?

• (0, 1)

• (1, 0)

• (1, 1)

• (0, 0)

What is the process of finding a unit vector called?

• Vectorization

• Normalization

• Linearization

• Magnification

How do you express a vector in terms of i and j?

• a - i + b - j

• a / i + b / j

• a * i + b * j

• a + b

What is the magnitude of the vector (4, -3)?

• 16

• 25

• 7

• 5

What is the x-component of a unit vector on the unit circle at angle θ?

• sin(θ)

• cos(θ)

• tan(θ)

• sec(θ)

If a vector is not a unit vector, how can its component form be determined?

• By multiplying by its magnitude

• By dividing by its magnitude

• By subtracting its magnitude

• By adding its magnitude

What is the angle between the positive x-axis and a unit vector forming a 120-degree angle?

• 30 degrees

• 90 degrees

• 120 degrees

• 60 degrees

What is the y-component of a unit vector at 120 degrees?

• 1/2

• -√3/2

• √3/2

• -1/2

How do you find a vector with the same direction as a unit vector but with a different magnitude?

• Add the magnitude to the unit vector

• Multiply the unit vector by the desired magnitude

• Divide the unit vector by the desired magnitude

• Subtract the magnitude from the unit vector