Distance between the two planes: and is

(A)2 units (B)4 units (C)8 units

(D)

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Solution

The equations of the planes are

It can be seen that the given planes are parallel.

It is known that the distance between two parallel planes, ax + by + cz = d₁ and ax + by + cz = d₂, is given by,

Thus, the distance between the lines is units.

Hence, the correct answer is D.

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Similar questions

Q. The distance between the planes

2 x + 3 y + 4 z = 4

and

4 x + 6 y + 8 z = 12

Choose the correct answer in Question
Distance between the two planes 2x + 3y + 4z = 4 and 4x + 6y+ 8z =12 is
(a) 2 units
(b) 4 units
(c) 8 units
(d) $\frac{2}{\sqrt{29}} u n i t s$

Q. The distance between the planes

2 x + 3 y + 4 z = 4

and

4 x + 6 y + 8 z = 12

(a) \frac{2}{\sqrt{29}} units (b) \frac{10}{\sqrt{29}} units

(c) 4 units (d) 2 units

Q. Distance between the two planes :

2 x + 3 y + 4 z = 4

and

4 x + 6 y + 8 z = 12

Q. Distance(in

units

) between the parallel planes

2 x - 3 y + 4 z - 1 = 0

and

4 x - 6 y + 8 z + 7 = 0

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Distance between the two planes: and is (A)2 units (B)4 units (C)8 units (D)

The equations of the planes are It can be seen that the given planes are parallel. It is known that the distance between two parallel planes, ax + by + cz = d1 and ax + by + cz = d2, is given by, Thus, the distance between the lines is units. Hence, the correct answer is D.

Distance between the two planes: and is

(A)2 units (B)4 units (C)8 units

(D)

The equations of the planes are

It can be seen that the given planes are parallel.

It is known that the distance between two parallel planes, ax + by + cz = d₁ and ax + by + cz = d₂, is given by,

Thus, the distance between the lines is units.

Hence, the correct answer is D.