a. Can a vector have nonzero magnitude if a component

Chapter 3, Problem 1

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QUESTION:

a. Can a vector have nonzero magnitude if a component iszero? If no, why not? If yes, give an example.b. Can a vector have zero magnitude and a nonzero component?If no, why not? If yes, give an example.

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QUESTION:

a. Can a vector have nonzero magnitude if a component iszero? If no, why not? If yes, give an example.b. Can a vector have zero magnitude and a nonzero component?If no, why not? If yes, give an example.

ANSWER:

Step 1 of 3

Part (a)

The magnitude of a vector can be expressed as,

                                                               

Here,  is the magnitude of a vector,  is the horizontal component and  is the vertical component.

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