Question

If two vectors have different magnitudes and opposite directions, what is the sum of the two vectors.

Answer 1

If two vectors have different magnitudes and opposite directions the sum of both the vectors will be a non-zero component.

Step-by-step explanation:

Let us assume that both the vectors lie in x-axis with the magnitudes of
`x_1` and
`x_2`. If the sum of the vectors are zero, i.e if
`x_1+x_2=0` then,
`x_1` will be equal to
`x_2` 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.