Vector Magnitudes and Operations

The video tutorial explains the concept of vectors, focusing on vector v with components x and y, and its magnitude. It introduces vector w as a scalar multiple of vector v, and vector z as a negative scalar multiple, discussing their magnitudes and directions. The tutorial includes example problems to illustrate these concepts, emphasizing the effects of scalar multiplication on vector magnitude and direction.

What is the x component of vector w if vector v is represented as (x, y)?

• 3y

• y

• 3x

• x

If vector v has a magnitude of 5, what is the magnitude of vector w?

• 5

• 10

• 15

• 20

How does the negative scalar affect the direction of vector z compared to vector v?

• No change

• Opposite direction

• Perpendicular direction

• Same direction

What is the magnitude of vector z if vector v has a magnitude of 5?

• 15

• 10

• 20

• 5

Which vector has the smallest magnitude among v, w, and z?

• All have the same magnitude

• v

• z

• w

If vector v has a magnitude of 10, what is the magnitude of vector w when multiplied by one-fifth?

• 15

• 2

• 5

• 10

What is the scalar used to multiply vector v to get vector z in the new scenario?

• 2/5

• 3/5

• 1/5

• 4/5

In the new scenario, which vector has the largest magnitude?

• w

• All have the same magnitude

• z

• v

What is the magnitude of vector z if vector v has a magnitude of 10 and is multiplied by three-fifths?

• 3

• 6

• 8

• 5

Which vector has the smallest magnitude in the new scenario?

• All have the same magnitude

• z

• w

• v