Show that the distance between the parallel planes ax+by+cz+d_1=0 and

sonkitty2h

sonkitty2h

Answered question

2021-11-20

Show that the distance between the parallel planes ax+by+cz+d1=0 and ax+by+cz+d2=0 is D=|d1d2|(a2+b2+c2)12

Answer & Explanation

Coldst

Coldst

Beginner2021-11-21Added 18 answers

The distance of the point (x1,y1,z1) from the plane ax+by+cz+d=0 is given by
D=ax1+by1+cz1+da2+b2+c2
If (x1,y1,z1) is a point on the first plane, then its distance from the second plane, then its distance from the second plane is given by
D=|ax1+by1+cz1+d2|a2+b2+c2
But (x1,y1,z1) is a point on the first plane, this means that we can write
ax1+by1+cz1+d1=0
Subtract d1 from both sides
ax1+by1+cz1=d1
Substitute this in
D=|d1+d2|a2+b2+c2
Hence proved.

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