Answer:
[tex]\displaystyle a = \frac{8}{5}[/tex].
Step-by-step explanation:
Two vectors [tex](x_1,\, y_1)[/tex] and [tex](x_2,\, y_2)[/tex] are parallel to one another if and only if the ratio between their corresponding components are equal:
[tex]\displaystyle \frac{x_1}{x_2} = \frac{y_1}{y_2}[/tex].
Equivalently:
[tex]\displaystyle \frac{x_1}{y_1} = \frac{x_2}{y_2}[/tex].
For the two vectors in this equation to be parallel to one another:
[tex]\displaystyle \frac{a}{4} = \frac{2}{5}[/tex].
Solve for [tex]a[/tex]:
[tex]\displaystyle a = \frac{8}{5}[/tex].
[tex]\displaystyle \frac{8}{5}[/tex] would be the only valid value of [tex]a[/tex]; no other value would satisfy the [tex]\displaystyle \frac{x_1}{y_1} = \frac{x_2}{y_2}[/tex] equation.
