Question 1206230
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A vector has magnitude 6.0 units due east, vector B points due north. Find
a) the magnitude of B if A+B points 60° north of east?
b) the magnitude of A+B
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        In this post, first sentence is incorrect.  Instead of  " A vector has magnitude  6.0  units due east, . . . "
       should be  " Vector  A  has magnitude  6.0  units due east, . . . ".


       It may seems like a small microscopic thing,  but in Math every word matters,  and the order 
        of the words does matters,  too.  Wrong order of words makes the post non-sensical.


        So,  I will solve the problem,  edited this way.



<pre>
(a)  Since in the coordinate plane vector A is vertical and vector B is horizontal, 

     vector A+B has x-component Ax = 6 = |A|, the magnitude of vector A, 
            and has y-component |B|, the magnitude of vector B.


     Since tan(60°) = {{{sqrt(3)}}},  it implies that  {{{abs(B)/6}}} = {{{sqrt(3)}}}.

     From this equation, we get |B| = {{{6*sqrt(3)}}} = 10.3923  (rounded).


     It gives the <U>ANSWER</U> to question (a) :  the magnitude of vector B is  {{{6*sqrt(3)}}} = 10.3923  (rounded).



(b)  Now we know that x-component of vector A+B is the same as x-component of vector A, i.e. 6,
     and we know that y-component of vector A+B is the same as y-component of vector B, i.e. {{{6*sqrt(3)}}}.

     Hence, the magnitude of A+B is  {{{sqrt(6^2 + (6*sqrt(3))^2)}}} = {{{sqrt(6^2+3*6^2)}}} = {{{sqrt(4*6^2)}}} = 2*6 = 12.


     It gives the <U>ANSWER</U> to question (b) :  the magnitude of A+B is 12.
</pre>

Solved.