Answer :
To convert the given equation \( a b = 2 c \) into the standard form \( ax + by + cz = 0 \), follow these steps:
1. Start with the original equation:
[tex]\[ a b = 2 c \][/tex]
2. Move all terms to one side of the equation to create a form where the equation is equal to zero. Subtract \( 2c \) from both sides:
[tex]\[ a b - 2 c = 0 \][/tex]
3. Compare the result with the given options:
[tex]\[ a b - 2 c = 0 \][/tex]
- Option A: \( a b - 2 c = 0 \)
- Option B: \( a b + 2 c = 0 \)
- Option C: \( 2 a + 2 b + 2 c = 0 \)
- Option D: \( 2 a b c = 0 \)
4. The equation \( a b - 2 c = 0 \) matches exactly with Option A.
Therefore, the equation \( a b = 2 c \) in standard form is represented by Option A:
[tex]\[ a b - 2 c = 0 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{1} \][/tex]
1. Start with the original equation:
[tex]\[ a b = 2 c \][/tex]
2. Move all terms to one side of the equation to create a form where the equation is equal to zero. Subtract \( 2c \) from both sides:
[tex]\[ a b - 2 c = 0 \][/tex]
3. Compare the result with the given options:
[tex]\[ a b - 2 c = 0 \][/tex]
- Option A: \( a b - 2 c = 0 \)
- Option B: \( a b + 2 c = 0 \)
- Option C: \( 2 a + 2 b + 2 c = 0 \)
- Option D: \( 2 a b c = 0 \)
4. The equation \( a b - 2 c = 0 \) matches exactly with Option A.
Therefore, the equation \( a b = 2 c \) in standard form is represented by Option A:
[tex]\[ a b - 2 c = 0 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{1} \][/tex]
