Answer :
To solve the problem of determining the correct relation among the given options, we can follow the relationships as described:
We start with the provided relation:
[tex]\[ 2l_1 = l_2 = 3l_3 \][/tex]
Let's express each variable based on these equalities:
1. If [tex]\( 2l_1 = l_2 \)[/tex] and [tex]\( l_2 = 3l_3 \)[/tex], we can deduce the following:
- From the first part, we have [tex]\( l_2 = 2l_1 \)[/tex].
- From the second part, since [tex]\( l_2 = 3l_3 \)[/tex], we can substitute [tex]\( 2l_1 \)[/tex] for [tex]\( l_2 \)[/tex] in the equation [tex]\( l_2 = 3l_3 \)[/tex] to get:
[tex]\[ 2l_1 = 3l_3 \][/tex]
Now, let's consider each of the provided choices and check if it matches our deduced relations:
(a) [tex]\( l_1 = 2l_1 = 3l_3 \)[/tex]:
- According to the deduced relation, same [tex]\( l_2 = 2l_1 \)[/tex] cannot be equal to [tex]\( 2l_1 \)[/tex] itself, and [tex]\( 3l_3 = l_2 \)[/tex], not [tex]\( l_1 \)[/tex].
- Hence, this is not a correct relationship.
(b) [tex]\( 3l_1 = 2l_2 = l_3 \)[/tex]:
- According to the deduced relation, [tex]\( 3l_3 = 2l_1 \)[/tex], not [tex]\( 2l_2 \)[/tex] and the relation here mismatches.
- So, this isn't correct as well.
(c) (Ignoring as it wasn't given in the original options)
(d) [tex]\( l_1 = 4l_2 = 3l_3 \)[/tex]:
- Deduced relations do not match because [tex]\( 2l_1 = l_2 \)[/tex] implies further mismatch with [tex]\( 4l_2 = l_1 \)[/tex].
- Hence, this isn't correct either.
Upon evaluation, none of the condition given in any of the options holds true based on our established relation [tex]\( 2l_1 = l_2 = 3l_3 \)[/tex].
Therefore, "No correct condition" is the final conclusion, meaning none of the options correctly represent the relationship between [tex]\( l_1, l_2, \)[/tex] and [tex]\( l_3 \)[/tex].
We start with the provided relation:
[tex]\[ 2l_1 = l_2 = 3l_3 \][/tex]
Let's express each variable based on these equalities:
1. If [tex]\( 2l_1 = l_2 \)[/tex] and [tex]\( l_2 = 3l_3 \)[/tex], we can deduce the following:
- From the first part, we have [tex]\( l_2 = 2l_1 \)[/tex].
- From the second part, since [tex]\( l_2 = 3l_3 \)[/tex], we can substitute [tex]\( 2l_1 \)[/tex] for [tex]\( l_2 \)[/tex] in the equation [tex]\( l_2 = 3l_3 \)[/tex] to get:
[tex]\[ 2l_1 = 3l_3 \][/tex]
Now, let's consider each of the provided choices and check if it matches our deduced relations:
(a) [tex]\( l_1 = 2l_1 = 3l_3 \)[/tex]:
- According to the deduced relation, same [tex]\( l_2 = 2l_1 \)[/tex] cannot be equal to [tex]\( 2l_1 \)[/tex] itself, and [tex]\( 3l_3 = l_2 \)[/tex], not [tex]\( l_1 \)[/tex].
- Hence, this is not a correct relationship.
(b) [tex]\( 3l_1 = 2l_2 = l_3 \)[/tex]:
- According to the deduced relation, [tex]\( 3l_3 = 2l_1 \)[/tex], not [tex]\( 2l_2 \)[/tex] and the relation here mismatches.
- So, this isn't correct as well.
(c) (Ignoring as it wasn't given in the original options)
(d) [tex]\( l_1 = 4l_2 = 3l_3 \)[/tex]:
- Deduced relations do not match because [tex]\( 2l_1 = l_2 \)[/tex] implies further mismatch with [tex]\( 4l_2 = l_1 \)[/tex].
- Hence, this isn't correct either.
Upon evaluation, none of the condition given in any of the options holds true based on our established relation [tex]\( 2l_1 = l_2 = 3l_3 \)[/tex].
Therefore, "No correct condition" is the final conclusion, meaning none of the options correctly represent the relationship between [tex]\( l_1, l_2, \)[/tex] and [tex]\( l_3 \)[/tex].
