Vector A, with magnitude 28.0 units, points in the positive y-direction. Vector A + B has a magnitude of 19.0 units and points in the −y-direction. What is the magnitude of B?

|B|  = 47.0 units

The sum of two vectors (A) and (B) gives another vector (A + B). i.e

(A + B) = (A) + (B)       (i)

From the question;

Vector A = 28.0 units in the positive y-direction. This means that the value of the x-component is zero and the value of the y-component is +28

In unit vector notation vector A is given as;

A = 0i + 28.0j

Vector A + B = 19.0 units in the negative y-direction. This means that the value of the x-component is zero and the value of the y-component is -19.0

In unit vector notation, vector A + B is given as;

A + B = 0i - 19.0j

To get the magnitude of vector B, make B the subject of the formula in equation (i) as follows;

(B) = (A + B) - (A)             (ii)

Substitute the values of the vectors (A) and (A + B) into equation (ii) as follows;

(B) = (0i - 19.0j) - (0i + 28.0j)

(B) = - 19.0j - 28.0j

(B) = - 47.0j

The magnitude of B, |B|, is therefore;

|B| = |-47.0|

|B| = 47.0 units

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