Vector Components and Representation

The video tutorial explains how to represent a vector using its x and y components, both as a column vector and in unit vector form. It demonstrates how to visualize a vector starting from the origin and moving to a terminal point. The tutorial also covers translating the vector to a new terminal point and calculating the initial point mathematically. Finally, it shows how to solve for initial and terminal points using vector components, emphasizing the relationship between these elements.

What are the x and y components of vector a?

• x = -10, y = 7

• x = 10, y = -7

• x = 7, y = -10

• x = -7, y = 10

How can vector a be represented in unit vector form?

• 7i - 10j

• 10i - 7j

• -7i + 10j

• -10i + 7j

Where does the vector start and end when its initial point is the origin?

• Starts at (0,0) and ends at (7,-10)

• Starts at (0,0) and ends at (-7,10)

• Starts at (0,0) and ends at (10,-7)

• Starts at (0,0) and ends at (-10,7)

If the terminal point of vector a is changed to (-3, 5), what happens to the vector?

• It rotates 90 degrees

• It remains unchanged

• It doubles in length

• It is translated to a new position

What is the initial point of vector a if its terminal point is (-3, 5)?

• (7, -2)

• (-7, 2)

• (3, -5)

• (-3, 5)

How do you calculate the x component of a vector given its initial and terminal points?

• Terminal x - Initial x

• Initial y - Terminal y

• Initial x - Terminal x

• Terminal y - Initial y

What is the y component of vector a if the initial y is -2 and the terminal y is 5?

• 7

• -7

• 3

• -3

What is the relationship between initial and terminal points and vector components?

• They are always equal

• They are independent

• Knowing two allows you to find the third

• All three must be known

If you know the initial point and vector components, what can you determine?

• The vector's length

• The initial point

• The terminal point

• The vector's angle

What can be determined if the terminal point and vector components are known?

• The vector's midpoint

• The vector's direction

• The initial point

• The vector's magnitude