SOLUTION: A vector pi+qj where p and q are scalars has its magnitude twice that of the vectors i+3j and is parallel to the vector 3i-4j. Find the vector.

Since vector pi+qj is parallel to the vector 3i-4j,  we can write

    pi + qj = a*(3i-4j).


where  "a"  is the scalar multiplier to the vector.


Next, the vector i+3j has the magnitude   = ,  according to the condition.


It means that   = ,    or


     = ,    or, equivalently,


    5a = ,

so

     a = 



THEREFORE,  pi + qj = .    ANSWER