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Question

If p1,p2,p3 denote the distances of the plane 2x - 3y + 4z + 2 = 0 from the planes 2x - 3y + 4z + 6 = 0, 4x - 6y + 8z + 3 = 0 and 2x - 3y + 4z - 6 = 0 respectively, then

A
p1+8p2p3=0
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B
p23=16p22
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C
8p22=p21
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D
p1+2p2+3p3=29
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Solution

The correct options are
A p1+8p2p3=0
D p1+2p2+3p3=29
Since the planes are all parallel planes, p1=|26|22+32+42=44+9+16=429
Equation of the plane 4x - 6y + 8z + 3 = 0 can be written as 2x3y+4z+32=0
So p2=23222+32+42=1229 and p3=|2+6|22+32+42=829p1+8p2p3=0

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