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? yes, if the two vectors are perpendicular. no, because of the angle between the two vectors. yes, if one of the vectors is zero. yes, if the two vectors are in the same direction. no, it is impossible for the magnitude of the sum to be equal to the sum of the magnitudes.

Yes, The sum of the magnitude of two vectors can be equal to the magnitude of the sum of the same two vectors. This situation can be apply when the two vector having same angle. the same two vectors when they both will be in same direction.

In this situation, the vector have the same proportion of  i and j components and therefor their magnitude also add linearly when they are added.

Let, consider the two vectors vector A and vector B

m of magnitude of two vectors = A + B

According to sum of vector formula,

magnitude of sum of two vectors can be given by,

From equation (1) and (2) can be only equal if

When the angle between both vectors is 0 ,

Where,

R = A + B

So, The sum of magnitude of two vector will be equal to magnitude of the sum of the same two vectors when they both will be in same direction.

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Step-by-step explanation:

sum of magnitude of two vectors = A+ B.......(1)

According to sum of vector formula,

magnitude of sum of two vectors can be given by,

equation (1) and (2) can be only equal if

Case 1:

Either or will be equal to 0.

Case 2:

The angle between both the vector will be 0.

When the angle between both vectors,

=> R = A+B

So, the sum of magnitude of two vector will be equal to magnitude of the sum of the same two vectors when they both will be in same direction.

1/4 because there is 4 grades.

step-by-step explanation: