Vector A has magnitude 8.00 mm and is in the xy-plane at an angle of 127∘ counterclockwise from the +x–axis (37∘ past the +y-axis). The sum A +B is in the −y-direction and has magnitude 12.0 mm. Find the vector B.

-75.35°

Explanation:

Let C be the sum of the two vectors A and B. Hence, we can write the following  

but since the vector C is in the -y direction,  = 0 and = —12 m.  

Thus  

similarly, we can determine by rearranging equation (1)  

so the magnitude of B is

Finally, the direction of B can be calculated as follows  

Ф=

hence the vector B makes an angle of 75.35 clockwise with + x axis

correct it is c.) b b

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