Question

Can the sum of the magnitudes of two vectors ever be equal to the magnitude of the sum of the same two vectors? If no, why not? If yes, when?

a-No, because of the angle between the two vectors.
b-No, it is impossible for the magnitude of the sum to be equal to the sum of the magnitudes.
c-Yes, if the two vectors are in the same direction.
d-Yes, if the two vectors are perpendicular.
e. Yes, if one of the vectors is zero.

Answer 1

c-Yes, if the two vectors are in the same direction.

e. Yes, if one of the vectors is zero.

Step-by-step explanation:

Lets take

The magnitude of the two vectors are A and B and they are at angle θ

Then the Sum of these two vectors

`\bar{R}=\bar{A}+\bar{B}`

Resultant R

`R=√(A^2+B^2+2ABcos\theta)`

if the angle between these vectors is zero.It means that they are in the same direction.

θ = 0

`R=√(A^2+B^2+2ABcos0)`

`R=√(A^2+B^2+2AB)`

`R=√((A+B)^2)`

R=A+B

If the one vector is zero vector.

Therefore the answer will be C and e.