Vector Magnitudes and Relationships

The video tutorial explores the relationship between vectors A, B, and C, where A plus B equals C. It poses questions about scenarios where the magnitude of vector C equals or exceeds the sum of magnitudes of A and B. The tutorial explains that the magnitude of C can only equal the sum of A and B if they are in the same direction, due to the triangle inequality. It also discusses how the magnitude of C is typically less than the sum of A and B when they are not aligned, using examples to illustrate these concepts.

What is the relationship between vectors A, B, and C as described in the introduction?

• Vector A minus vector B equals vector C

• Vector A plus vector B equals vector C

• Vector A times vector B equals vector C

• Vector A divided by vector B equals vector C

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CCSS.HSN-VM.B.4B

CCSS.HSN-VM.B.4A

In what scenario can the magnitude of vector C be equal to the sum of magnitudes of vectors A and B?

• When vectors A and B form a right angle

• When vectors A and B are perpendicular

• When vectors A and B are in opposite directions

• When vectors A and B are in the same direction

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CCSS.HSN-VM.B.4B

CCSS.HSN-VM.B.4A

What is the condition for the magnitude of vector C to be exactly the sum of magnitudes of vectors A and B?

• Vectors A and B must be parallel

• Vectors A and B must be zero

• Vectors A and B must be perpendicular

• Vectors A and B must be equal

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CCSS.HSN.VM.A.3

Why is it impossible for the magnitude of vector C to be greater than the sum of magnitudes of vectors A and B?

• Because vectors A and B are always equal

• Because magnitudes are always equal

• Because vectors cannot be added

• Because of the triangle inequality

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CCSS.HSN-VM.B.4B

CCSS.HSN-VM.B.4A

What geometric shape do vectors A, B, and C form when added?

• Rectangle

• Square

• Circle

• Triangle

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CCSS.HSN-VM.B.4C

What typically happens to the magnitude of vector C when vectors A and B are not aligned?

• It becomes zero

• It becomes equal to the sum of magnitudes of A and B

• It becomes greater than the sum of magnitudes of A and B

• It becomes less than the sum of magnitudes of A and B

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CCSS.HSN-VM.B.4C

What happens to vector C's magnitude if vectors A and B are in opposite directions?

• It becomes the product of magnitudes of A and B

• It becomes zero

• It becomes the sum of magnitudes of A and B

• It becomes the difference of magnitudes of A and B

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CCSS.HSN-VM.B.4C

What is the typical scenario when vectors A and B are not in the same direction?

• The magnitude of vector C is greater than the sum of magnitudes of A and B

• The magnitude of vector C is less than the sum of magnitudes of A and B

• The magnitude of vector C is equal to the sum of magnitudes of A and B

• The magnitude of vector C is zero

If the magnitude of vector A is 5 and vector B is 3, what is the maximum possible magnitude of vector C?

• 8

• 3

• 10

• 5

In the example given, what is the condition for vector C's magnitude to reach 8?

• Vectors A and B must be perpendicular

• Vectors A and B must be in the same direction

• Vectors A and B must be in opposite directions

• Vectors A and B must be equal