Vector Components and Terminal Points

The video tutorial explains how to find the terminal point of a vector given its components and initial point. It first demonstrates the process graphically by plotting the vector in standard position and then moving it to the specified initial point. The tutorial then explains an algebraic method to calculate the terminal point by solving equations derived from the vector's components. Both methods lead to the same terminal point, providing a comprehensive understanding of vector translation.

What are the components of the given vector v?

• X component: 3, Y component: -1

• X component: 4, Y component: -2

• X component: -2, Y component: 4

• X component: 2, Y component: -4

Where is the initial point of vector v located?

• At point (0, 0)

• At point (-2, 3)

• At point (4, -2)

• At the origin

How do you find the terminal point graphically from the initial point (-2, 3)?

• Move right 2 units and up 4 units

• Move left 2 units and down 4 units

• Move right 4 units and down 2 units

• Move left 4 units and up 2 units

What is the equivalent vector with the initial point at (-2, 3)?

• A vector with X component 0 and Y component 0

• A vector with X component -4 and Y component 2

• A vector with X component 4 and Y component -2

• A vector with X component 2 and Y component 1

What is the algebraic expression for the X component of the terminal point?

• x2 + 2 = 4

• x2 - 2 = 4

• x2 + 4 = 2

• x2 - 4 = 2

What is the algebraic expression for the Y component of the terminal point?

• y2 - 2 = 3

• y2 + 2 = 3

• y2 + 3 = -2

• y2 - 3 = -2

What is the value of x2 after solving the equation?

• x2 = 0

• x2 = -2

• x2 = 4

• x2 = 2

What is the value of y2 after solving the equation?

• y2 = -3

• y2 = 3

• y2 = -1

• y2 = 1

What is the terminal point of vector v?

• (0, 0)

• (2, 1)

• (-2, 3)

• (4, -2)

Which method can be used to find the terminal point of a vector?

• Algebraic method only

• Both graphical and algebraic methods

• Neither graphical nor algebraic methods

• Graphical method only