Question

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

• A. $0$
• B. exactly one
• C. exactly two
• D. infinite

Answer 1

Answer: (D)

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.