Question

Find all constants a such that the vectors (a, 4) and (2, 5) are parallel.

Answer 1

`\displaystyle a = (8)/(5)`.

Explanation:

Two vectors
`(x_1,\, y_1)` and
`(x_2,\, y_2)` are parallel to one another if and only if the ratio between their corresponding components are equal:

`\displaystyle (x_1)/(x_2) = (y_1)/(y_2)`.

Equivalently:

`\displaystyle (x_1)/(y_1) = (x_2)/(y_2)`.

For the two vectors in this equation to be parallel to one another:

`\displaystyle (a)/(4) = (2)/(5)`.

Solve for
`a`:

`\displaystyle a = (8)/(5)`.

`\displaystyle (8)/(5)` would be the only valid value of
`a`; no other value would satisfy the
`\displaystyle (x_1)/(y_1) = (x_2)/(y_2)` equation.