Understanding Equivalent Vectors

The video tutorial explores the concept of equivalent vectors, focusing on their magnitude and direction. It begins with an introduction to vectors and their properties, followed by a detailed analysis of vector directions. The tutorial then demonstrates how to calculate vector magnitudes using the Pythagorean theorem. It compares the magnitudes of two vectors, u and w, and verifies their equivalence by examining their components. The tutorial concludes by confirming the equivalence of vectors through their x and y components.

What are the two main characteristics that define a vector?

• Height and depth

• Length and width

• Magnitude and direction

• Speed and velocity

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CCSS.HSN.VM.A.1

Why are vectors u and w not equivalent in the first example?

• They have different magnitudes

• They have different directions

• They have different initial points

• They have different terminal points

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CCSS.HSN.VM.A.1

How is the magnitude of a vector calculated using its components?

• By adding the components

• By using the Pythagorean theorem

• By multiplying the components

• By subtracting the components

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CCSS.HSN.VM.A.1

What is the magnitude of vector u in the example provided?

• Square root of 25

• Square root of 50

• Square root of 36

• Square root of 61

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CCSS.HSN.VM.A.1

What is the magnitude of vector w in the example provided?

• Square root of 50

• Square root of 25

• Square root of 36

• Square root of 61

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CCSS.HSN-VM.B.5A

CCSS.HSN-VM.B.5B

What conclusion can be drawn if two vectors have the same magnitude but different directions?

• They are equivalent

• They are not equivalent

• They are parallel

• They are perpendicular

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CCSS.HSN.VM.A.1

In the second example, what is the change in x for vector u?

• Positive 3

• Positive 5

• Negative 5

• Negative 3

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CCSS.HSN-VM.B.4A

CCSS.HSN-VM.B.4B

In the second example, what is the change in y for vector w?

• Negative 3

• Positive 5

• Negative 5

• Positive 3

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CCSS.HSN.VM.A.1

What does it mean if two vectors have the same change in x and y?

• They are opposite

• They are perpendicular

• They are not equivalent

• They are equivalent

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CCSS.HSN.VM.A.2

How can a vector be denoted using its components?

• By its speed and velocity

• By its change in x and change in y

• By its initial and terminal points

• By its length and width

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CCSS.HSN.VM.A.2