Vector Scaling and Properties

The video tutorial explains scalar multiplication of vectors, focusing on how multiplying a vector by a scalar affects its components, magnitude, and direction. It provides examples of multiplying vector v by one-third and negative two, demonstrating the changes in vector properties. The tutorial emphasizes that scalar multiplication alters magnitude but not direction unless the scalar is negative, which reverses the direction.

What are the initial and terminal points of vector v?

• (0, 0) and (6, 9)

• (1, 1) and (5, 8)

• (2, 3) and (4, 7)

• (0, 0) and (3, 6)

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CCSS.HSN-VM.B.5A

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How do you perform scalar multiplication on a vector?

• Subtract the scalar from each component

• Divide each component by the scalar

• Multiply each component by the scalar

• Add the scalar to each component

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What is the x component of the vector after scaling by one-third?

• 1

• 3

• 4

• 2

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CCSS.HSN-VM.B.5A

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What happens to the direction of a vector when it is scaled by a positive scalar?

• It reverses

• It remains unchanged

• It rotates 90 degrees

• It becomes perpendicular

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If a vector is scaled by a factor between zero and one, what happens to its magnitude?

• It decreases

• It increases

• It doubles

• It remains the same

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CCSS.HSN.VM.A.1

What color represents the original vector v on the coordinate plane?

• Yellow

• Blue

• Green

• Red

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What is the effect of a negative scalar on the direction of a vector?

• It rotates 45 degrees

• It reverses

• It becomes parallel

• It remains unchanged

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What is the y component of the vector after scaling by negative two?

• -6

• 6

• -3

• 3

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How does the magnitude of a vector change when scaled by a factor greater than one?

• It decreases

• It remains the same

• It increases

• It becomes zero

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What is the x component of the vector after scaling by negative two?

• -4

• 4

• 2

• -2

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CCSS.HSN-VM.B.5A

CCSS.HSN-VM.B.5B