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m_a_m_a [10]
3 years ago
10

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

Mathematics
1 answer:
Nezavi [6.7K]3 years ago
4 0

Answer:

\displaystyle a = \frac{8}{5}.

Step-by-step 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 \frac{x_1}{x_2} = \frac{y_1}{y_2}.

Equivalently:

\displaystyle \frac{x_1}{y_1} = \frac{x_2}{y_2}.

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

\displaystyle \frac{a}{4} = \frac{2}{5}.

Solve for a:

\displaystyle a = \frac{8}{5}.

\displaystyle \frac{8}{5} would be the only valid value of a; no other value would satisfy the \displaystyle \frac{x_1}{y_1} = \frac{x_2}{y_2} equation.

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