To determine which of the given options is correct, we need to understand the relationship between the variables [tex]\( v \)[/tex], [tex]\( \lambda \)[/tex], and [tex]\( c \)[/tex]. The answer is obtained through logical reasoning and understanding the physical principles that these symbols might represent in standard equations.
1. Option 1: [tex]\( v + \lambda = c \)[/tex]
- This suggests that the sum of [tex]\( v \)[/tex] and [tex]\( \lambda \)[/tex] equals [tex]\( c \)[/tex]. This is a simple linear equation, but it doesn’t fit any common physics or mathematics relationships involving these symbols.
2. Option 2: [tex]\( \frac{v}{\lambda} = c \)[/tex]
- This implies that [tex]\( v \)[/tex] divided by [tex]\( \lambda \)[/tex] results in [tex]\( c \)[/tex]. While this could be a potential relationship, it doesn't immediately point to a well-known formula.
3. Option 3: [tex]\( v = c \lambda \)[/tex]
- This suggests that [tex]\( v \)[/tex] equals [tex]\( c \)[/tex] multiplied by [tex]\( \lambda \)[/tex]. This aligns with the form of many standard equations in physics and mathematics where one variable is the product of a constant and another variable.
4. Option 4: [tex]\( \lambda = c v \)[/tex]
- This equates [tex]\( \lambda \)[/tex] to the product of [tex]\( c \)[/tex] and [tex]\( v \)[/tex]. While feasibly correct, it is often conventional to express relationships in terms of the dependent variable first, if possible.
5. Option 5: [tex]\( v \lambda = c \)[/tex]
- This implies that the product of [tex]\( v \)[/tex] and [tex]\( \lambda \)[/tex] equals [tex]\( c \)[/tex]. While this could be correct in the context of some specific scenarios, it does not represent a common standard relationship generally.
Upon evaluation of these options and reflecting on standard relationships for such variables, the correct and most logical choice appears to be:
Option 3: [tex]\( v = c \lambda \)[/tex]
This form is representative of many typical relational equations in physics, where one variable is the product of another variable and a constant. This relationship is straightforward and aligns well with standard representations. Therefore, the correct answer is:
[tex]\[
\boxed{3}
\][/tex]
