Question

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

Answer 1

`\alpha_(2) = (5)/(4)\cdot \alpha_(1)`, for all
`\alpha_(1) \in \mathbb{R}`

Explanation:

Vectors are parallel to each other if:

`\vec u = \beta \cdot \vec v`

`(\alpha_(2), 5) = (\beta\cdot \alpha_(1), \beta \cdot 4)`

The value of
`\beta` is:

`\beta = (5)/(4)`

Then, the following relationship is found:

`\alpha_(2) = (5)/(4)\cdot \alpha_(1)`, for all
`\alpha_(1) \in \mathbb{R}`