Question 578147

u=-i+2j    v=3i+5j

w= (-i+2j) + 2(3i+5j) 
w1= -i + 2j + 6i + 10j = 5i + 12j

M(w1) = sqrt(25+144) = 13, this is exactly half the desired magnitude, thus we need to multiply w1 by 2 to get w

w = 10i 24j

CHECK:

M(w) = sqrt(100+576) = sqrt(676) = 26√