Question
Question: Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 (A). \(\dfrac{5}{2}\...
Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0
(A). 25
(B). 27
(C). 29
(D). 23
Solution
Before attempting this question, one should have prior knowledge about the concept of planes and also remember to consider the equal of plane i.e. 4x + 2y + 4z + 5 = 0 as equation 2 and divide it by 2, using this information can help you to approach the solution of the question.
Complete step-by-step answer :
According to the given information we have 2 planes parallel to each other represented by the equations 2x + y + 2z = 8 and 4x + 2y + 4z = - 5
Taking 2x + y + 2z = 8 as equation 1 and 4x + 2y + 4z = -5 as equation 2
Now dividing equation 2 by 2 we get
24x+22y+24z=2−5
⇒ 2x+y+2z=2−5
As we know that distance between two parallel planes is given by d=A2+B2+C2∣D2−D1∣
Also, we know that A = 2, B = 1 and C = 2 also D1=8 and D2=2−5
Now substituting the values in the distance formula, we get
Distance between two parallel planes = (2)2+(1)2+(2)28−(−25)
⇒ Distance between two parallel planes = 4+1+48+25
⇒ Distance between two parallel planes = 9216+5
⇒ Distance between two parallel planes = 2×321
⇒ Distance between two parallel planes = 621=27
Therefore, the distance between the two parallel planes 27
Hence, option B is the correct option.
Note : In the above solution we came across the two terms ``plane” which can be explained as a flat surface which is a two-dimensional surface which is constructed by the combination of two axis such as the combination of x axis and y axis will be x-y plane. Equation of a plane is represented by ax + by + cz = d and this is named as the scalar equation of the plane.