Understanding Vectors: Component Form and Magnitude

This video tutorial covers the basics of vectors, focusing on writing component forms and finding magnitudes. It includes detailed examples of vectors PQ, V, and AB, demonstrating how to calculate their component forms and magnitudes using the Pythagorean theorem. The tutorial also explores scalar multiples with vector BC, providing a comprehensive understanding of vector operations on a Cartesian coordinate plane.

What is the component form of vector PQ if P is at (2, -3) and Q is at (-5, 4)?

• (5, -5)

• (-5, 5)

• (7, -7)

• (-7, 7)

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CCSS.HSN.VM.A.1

How do you calculate the magnitude of a vector with components (-7, 7)?

• Square root of 98

• Square root of 14

• Square root of 49

• Square root of 2

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CCSS.HSN.VM.A.2

What is the component form of vector V if its initial point is (2, 3) and terminal point is (8, 6)?

• (6, 3)

• (3, 6)

• (-6, -3)

• (-3, -6)

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CCSS.HSN.VM.A.1

How do you find the magnitude of a vector with components (6, 3)?

• Square root of 18

• Square root of 9

• Square root of 36

• Square root of 45

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CCSS.HSN.VM.A.2

What is the component form of vector AB if A is at (1, 1) and B is at (-2, 4)?

• (3, -3)

• (-1, 1)

• (-3, 3)

• (1, -1)

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CCSS.HSN.VM.A.1

How do you calculate the magnitude of vector AB with components (-3, 3)?

• Square root of 18

• Square root of 3

• Square root of 9

• Square root of 6

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CCSS.HSN-VM.B.5A

CCSS.HSN-VM.B.5B

If vector BC has components (5, -8), what is the component form when it is doubled?

• (20, -32)

• (5, -8)

• (10, -16)

• (15, -24)

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CCSS.HSN.VM.A.1

What is the magnitude of vector 2BC with components (10, -16)?

• Square root of 256

• Square root of 356

• Square root of 100

• Square root of 144

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CCSS.HSN-VM.B.5A

CCSS.HSN-VM.B.5B

What happens to the components of a vector when it is multiplied by a scalar?

• They are divided by the scalar

• They remain unchanged

• They are multiplied by the scalar

• They are added to the scalar

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CCSS.HSN.VM.A.2

How do you find the component form of a vector given its initial and terminal points?

• Multiply the initial point by the terminal point

• Subtract the initial point from the terminal point

• Divide the terminal point by the initial point

• Add the initial and terminal points

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CCSS.HSN.VM.A.2