This picture develops a clear understanding.
The two vectors (say A and B) of different magnitudes cannot be combined to give zero resultant since minimum value of combination is ІA-BІ which is not zero if AB.
The three vectors A, B and C of different magnitudes can be zero such that they form a closed triangle, then,
A+B+C=0
or, C=-(A+B)
Hence, the sum of three vectors may be zero if vector sum of any two vectors is equal and opposite to the third vector.
Note: The vectors can give this result only if...
Here, f: A—>B
f(x)= (x-1)/(x+2) ; x -2
A= {-1,0,1,2,3,4}
B= {-2,1,-1/2,0,1/2,1/4,2/5}
Range = {-2,-1/2,0,1/4,1/2,2/5}
As range is not equal to codomain so the given function is not bijective.
We can make it bijective by omitting {1} from set B
It is theoretically possible for a substance to have a negative value of cubical expansivity, which means that the substance would contract rather than expand when the temperature increases. However, it is very rare for a substance to have a negative value of cubical expansivity over a significant range of temperatures.
One example of a substance that has a negative value of cubical expansivity over a limited range of temperatures is water. Water has a positive value of cubical expansivity at...
