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## 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-dir

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## Answers ( )

Answer:|B| = 47.0 units

Explanation: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 +28In unit vector notation vector

Ais given as;A =0i + 28.0jVector

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 -19.0In unit vector notation, vector

A + Bis given as;A + B =0i – 19.0jTo get the magnitude of vector

B,makeBthe 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(B) =– 47.0jThe magnitude of B, |B|, is therefore;

|B| = |-47.0|

|B| = 47.0 units