Concept:A line can be represented as the intersection of two planes.
The point that lies on the line must satisfy both plane equations.
Explanation:The given line is
2x−1​=3y−2​=4z−3​.
So it passes through the point
P(1,2,3).
For the line to be represented by a pair of planes,
P must satisfy both plane equations.
Check each option by substituting
(1,2,3).
Option A:
x+y+z=6 and
x+2y−3z=−4.
1+2+3=6 (true),
1+4−9=−4 (true).
Both equations are satisfied.
Option B:
x+2y−2z=−1 and
4x+4y−5z−3=0.
1+4−6=−1 (true), but
4+8−15−3=−6î€ =0 (false).
Option C:
3x+2y−3z=0 and
3x−6y+3z=−2.
3+4−9=−2î€ =0 (false).
Option D:
3x+2y−3z=−2 and
3x−6y+4z=0.
3+4−9=−2 (true), but
3−12+12=3î€ =0 (false).
Only Option A satisfies the point condition for both planes.
Hence, that pair represents the given line.
Answer:Option A.