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. 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. 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.
Expert Solution
To determine
A vector have a nonzero magnitude if a component is zero.
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
v→ and components of
v→ be
v1,v2,v3,.....vn.
Write the expression to find the magnitude of vector.
|v→|=v12+v22+v32+...+vn2
So, Magnitude of vector
|v→| is zero if and only iff all the components are zero. If any one of the component result with non zero, then vector will have nonzero magnitude.
Example:
Consider the two dimensional vector as follows.
v→=5i + 0j
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.
Expert Solution
To determine
A vector have a zero magnitude and a nonzero component.
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.
v→=v1i+v2j+v3k
Find the magnitude of vector
v→.
|v→|=v12+v22+v32
From the above expression, if
v1+v2+v3 is non zero value, then magnitude of
v→ will also be non zero.
Conclusion:
Hence, cannot have zero magnitude with non zero component is explained.
Want to see more full solutions like this?
Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Imagine you are out for a stroll on a sunny day when you encounter a lake. Unpolarized light from the sun is reflected off the lake into your eyes. However, you notice when you put on your vertically polarized sunglasses, the light reflected off the lake no longer reaches your eyes. What is the angle between the unpolarized light and the surface of the water, in degrees, measured from the horizontal? You may assume the index of refraction of air is nair=1 and the index of refraction of water is nwater=1.33 . Round your answer to three significant figures. Just enter the number, nothing else.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.