The equation of the plane passing through the points (2,3,40) and (−1,1,−7) and perpendicular to the plane x−2y+5z+1=0 is:
4x+7y+2z+11=0
Required plane is perpendicular to the given plane
x−2y+5z+1=0
⇒ Required plane is parallel to the line which is perpendicular to the given plane.
Direction ratio of line a=1,b=−2,c=5.
Hence required plane is
I x-x₁ y-y₁ z-z₁
x₂-x₁ y₂-y₁ z₂-z₁ = 0
a b c I
⇒ I x-2 y+3 z-1
-1-2 1+3 -7-1 = 0
1 -2 5 I
⇒ I x-2 y+3 z-1
-3 4 -8 = 0
1 -2 5 I
⇒(x−2)(20−16)−(y+3)(−15+8)+(z−1)(6−4)=0
⇒(x−2)4−(y+3)(−7)+(z−1)2=0
⇒4x+7y+2z+11=0
Hence we get the required equation.
Learn more about Equation of a line here:
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