Distance between the two planes: and is (A)2 units (B)4 units (C)8 units (D)
The equations of the planes are,
2 x + 3 y + 4 z = 4 (1)
4 x + 6 y + 8 z = 12 2 x + 3 y + 4 z = 6 (2)
The given planes are parallel to each other.
The formula for the distance between two planes A x + B y + C z + d 1 = 0 and A x + B y + C z + d 2 = 0 is given by,
d = | d 2 − d 1 A 2 + B 2 + C 2 |
Here,
A = 2 , B = 3 , C = 4 d 1 = 4 d 2 = 12
Substitute the values in the above expression.
d = | 6 − 4 ( 2 ) 2 + ( 3 ) 2 + ( 4 ) 2 | = | 2 4 + 9 + 16 | d = 2 29
Thus, the distance between the planes is 2 29 .
The correct option is (D).
The equations of the planes are,
The given planes are parallel to each other.
The formula for the distance between two planes
Here,
Substitute the values in the above expression.
Thus, the distance between the planes is
The correct option is (D).
and
is