Concept explainers
a. Can a vector have nonzero magnitude if a component is zero? 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.
a.
Answer to Problem 1CQ
Vector can have nonzero magnitude if a component is zero is explained with an example.
Explanation of Solution
Let, Vector be
Write the expression to find the magnitude of vector.
So, Magnitude of vector
Example:
Consider the two dimensional vector as follows.
In this vector the y component is 0 but still the magnitude is 5. A vector only has zero magnitude when all its components are 0.
Thus, vector can have nonzero magnitude if a component is zero.
Conclusion:
Hence, vector can have nonzero magnitude if a component is zero is explained with an example.
b.
Answer to Problem 1CQ
Vector cannot have zero magnitude with non zero component is explained.
Explanation of Solution
As explained in part (a), the magnitude of vector is zero if and only iff all the components is zero. If any of the component is nonzero then magnitude of the vector result with nonzero.
Therefore vector cannot have zero magnitude with non zero component.
Example:
Consider a vector as follows.
Find the magnitude of vector
From the above expression, if
Conclusion:
Hence, cannot have zero magnitude with non zero component is explained.
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