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Q.
Consider the planes $P_{1}:2x-y+2z=1,P_{2}:x+2y-z=2$ and $P_{3}:3x+6y-3z=6$ . Then the number of point(s) where plane $P_{1},P_{2}$ and $P_{3}$ intersect is/are
NTA AbhyasNTA Abhyas 2022
Solution:
We have,
$P_{1}:2x-y+2z=1$
$P_{2}:x+2y-z=2$
$P_{3}:3x+6y-3z=6$
or $P_{3}:x+2y-z=2$
Plane $P_{2}:x+2y-z=2$ and $P_{3}:3x+6y-3z=6$ are same.
Now, we have two planes $P_{1}$ and $P_{2}$ and they intersect and the line of intersection of two planes has infinite point. Hence, $P_{1}$ and $P_{2}$ intersect at infinite points.