Question

Which is enough information to prove that u|| V?
A) 5/6
B) 12
C) 817
D) 3

Answer 1

The value sufficient to prove that the vectors
`\( \mathbf{u} \) and \( \mathbf{v} \)` are parallel is B) 12.

Step-by-step explanation:

To determine if vectors
`\( \mathbf{u} \)` and
`\( \mathbf{v} \)` are parallel, we can compare their scalar multiples. Two vectors are parallel if one is a scalar multiple of the other, i.e.,
`\( \mathbf{u} = k \cdot \mathbf{v} \)`, where \( k \) is a constant. In this case, the scalar multiple is provided in option B) 12. Therefore, if
`\( \mathbf{u} = 12 \cdot \mathbf{v} \)`, the vectors are indeed parallel.

Now, let's consider the other options:

- A)
`\( (5)/(6) \)`: This fraction is not a whole number, making it insufficient to establish a clear scalar multiple relationship.

- C) 817: This large number is not necessary to determine vector parallelism. A scalar multiple can be any constant value, and 817 does not provide a more conclusive result than the simpler option.

- D) 3: Similar to option A), the value 3 is not sufficient to ensure a clear scalar multiple relationship between
`\( \mathbf{u} \)` and
`\( \mathbf{v} \)`.

Therefore, the correct and sufficient information to prove that
`\( \mathbf{u} \)` and
`\( \mathbf{v} \)` are parallel is given by option B) 12.

Complete Question:

What value or information is sufficient to establish that vectors u and v are parallel (denoted as u || v) in a vector space?

A) 5/6

B) 12

C) 817

D) 3