Q1 of 230 Page 30

Find the distance between the parallel planes 2x – y + 3z – 4 = 0 and 6x – 3y + 9z + 13 = 0.

Let P(x1,y1,z1) be any point on 2x – y + 3z – 4 = 0.


⟹ 2x1 – y1 + 3z1 – 4 = 0


⟹ 2x1 – y1 + 3z1 = 4 eq(i)


Distance between (x1,y1,z1) and the plane


6x – 3y + 9z + 13 = 0:


We know, the distance of point (x1,y1,z1) from the plane


is given by:



Putting the necessary values,


⟹


⟹


⟹ (using eq (i) )


⟹


∴ the distance between the parallel planes 2x – y + 3z – 4 = 0 and


6x – 3y + 9z + 13 = 0 is units.


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