Vector Analysis and Unit Vectors

The video tutorial explains how to find the component form of a vector given its initial and terminal points. It then demonstrates how to calculate the unit vector in the direction of the given vector by normalizing it. The process involves calculating the vector's magnitude and using it to scale the vector components. The tutorial concludes with a visual representation of the vectors in space, highlighting the equivalence of the original and component vectors, and the direction of the unit vector.

What is the initial point of vector v?

• (-3, -5, 3)

• (-2, 1, 1)

• (0, 0, 0)

• (1, -6, -2)

How do you find the X component of vector v?

• Multiply the X coordinates of the initial and terminal points

• Subtract the X coordinate of the initial point from the terminal point

• Divide the X coordinate of the terminal point by the initial point

• Add the X coordinates of the initial and terminal points

What is the Y component of vector v after simplification?

• 1

• -6

• 5

• 0

What is the formula for the magnitude of a vector?

• Difference of the components

• Sum of the components

• Square root of the sum of the squares of the components

• Product of the components

What is the magnitude of vector v?

• Square root of 36

• Square root of 4

• Square root of 41

• Square root of 1

How is the unit vector in the direction of vector v calculated?

• By adding 1 to each component of vector v

• By dividing each component of vector v by its magnitude

• By subtracting 1 from each component of vector v

• By multiplying each component of vector v by its magnitude

What is the X component of the unit vector in the direction of vector v?

• 0

• 1 / sqrt(41)

• -6 / sqrt(41)

• 2 / sqrt(41)

What is the Y component of the unit vector in the direction of vector v?

• 2 / sqrt(41)

• -6 / sqrt(41)

• 1 / sqrt(41)

• 0

What is the Z component of the unit vector in the direction of vector v?

• 0

• 2 / sqrt(41)

• -6 / sqrt(41)

• 1 / sqrt(41)

What does the red vector represent in the visualization?

• A random vector

• The original vector v

• The sum of vector v and the unit vector

• The unit vector in the direction of vector v