Question

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

Answer 1

Answer:

$\alpha_{2} = \frac{5}{4}\cdot \alpha_{1}$, for all $\alpha_{1} \in \mathbb{R}$

Step-by-step 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:

$\beta = \frac{5}{4}$

Then, the following relationship is found:

$\alpha_{2} = \frac{5}{4}\cdot \alpha_{1}$, for all $\alpha_{1} \in \mathbb{R}$