Respuesta :

As per given by the question,

There are given that the vector,

[tex]w=-\frac{1}{2}i-\frac{3}{2}j[/tex]

Now,

If the another value is given;

[tex]-\frac{9}{2}w[/tex]

Then,

[tex]\begin{gathered} -\frac{9}{2}w=-\frac{9}{2}(-\frac{1}{2}i-\frac{3}{2}j) \\ =(-\frac{9}{2}(-\frac{1}{2}i)+\frac{9}{2}(\frac{3}{2}j)) \\ =\frac{9}{4}i+\frac{27}{4}j \end{gathered}[/tex]

Hence, the option first is correct.