Vector Magnitude and Unit Vectors

The video tutorial explains how to find the component form of a vector given its initial and terminal points. It demonstrates sketching the vector on a coordinate plane and calculating its X and Y components. The tutorial then covers determining a unit vector in the same direction by calculating the vector's magnitude and performing scalar multiplication. Finally, it presents the results graphically, showing the original vector and the unit vector.

What are the initial and terminal points of vector v?

• (4, -2) and (1, 3)

• (1, 3) and (4, -2)

• (0, 0) and (1, 3)

• (4, -2) and (0, 0)

How many units do you move left to go from the initial to the terminal point of vector v?

• 2 units

• 3 units

• 4 units

• 5 units

What is the Y component of vector v in component form?

• -3

• 5

• 3

• -5

What is the formula to calculate the magnitude of a vector?

• Sum of the components

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

• Difference of the components

• Product of the components

What is the magnitude of vector v?

• 34

• 5

• 9

• √34

How do you find a unit vector in the direction of a given 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 X component of the unit vector in the direction of vector v?

• 5/√34

• 3/√34

• -5/√34

• -3/√34

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

• 5/√34

• -3/√34

• 3/√34

• -5/√34

Which color represents the unit vector in the graphical representation?

• Red

• Green

• Yellow

• Blue

What is the magnitude of the unit vector?

• 5

• 0

• 1

• √34