If two vectors have different magnitudes and opposite directions the sum of both the vectors will be a non-zero component.
Explanation:
Let us assume that both the vectors lie in x-axis with the magnitudes of [tex]x_1[/tex] and [tex]x_2[/tex]. If the sum of the vectors are zero, i.e if [tex]x_1+x_2=0[/tex] then, [tex]x_1[/tex] will be equal to [tex]x_2[/tex] which generally states that the vectors are of same magnitude.
So, from this we can come to a conclusion that the sum of two vectors with different magnitudes and opposite directions will not be zero.
Additional information: In contrast to the sum, the dot-product of two vectors have different magnitudes and opposite directions will be zero.
