Vector Components and Scalar Multiplication

The video tutorial explains how to sketch and calculate scalar multiples of vectors. It begins with vectors A and B, detailing their components. The tutorial demonstrates sketching 3 times Vector A and -2 times Vector B by hand, explaining the process of multiplying vector components by scalars. Finally, it uses an online graphing tool to sketch -3 times Vector W, providing a step-by-step guide to using the tool effectively.

What are the components of vector A?

• X: 2, Y: 1

• X: 0, Y: 3

• X: 1, Y: 2

• X: -3, Y: 1

How do you graphically represent 3 times vector A?

• Move left three and down one, three times

• Move right three and down one, three times

• Move left one and up two, three times

• Move right one and up two, three times

What is the X component of 3 times vector A?

• 2

• 1

• 3

• 6

What is the Y component of 3 times vector A?

• 4

• 6

• 2

• 8

How does the direction of -2 times vector B compare to vector B?

• Same direction

• Opposite direction

• Perpendicular direction

• No direction

What is the X component of -2 times vector B?

• -6

• 6

• -3

• 3

What is the Y component of -2 times vector B?

• -1

• -2

• 1

• 2

What are the components of vector W?

• X: -2, Y: 1

• X: 1, Y: -2

• X: -1, Y: 2

• X: 2, Y: -1

How do you graphically represent -3 times vector W?

• Move left three and down one, three times

• Move left one and up two, three times

• Move right one and down two, three times

• Move right three and up one, three times

What is the effect of multiplying a vector by a negative scalar?

• Decreases magnitude and reverses direction

• Increases magnitude and keeps direction

• Increases magnitude and reverses direction

• Decreases magnitude and keeps direction