Family of Planes Passing through the Intersection of Two Planes
Equation of t...
Question
Equation of the plane which passes through the point (-1, 3, 2) & is ⊥ to each of the planes p1 & p2 is
A
2x+y+z+1=0
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B
3x+8y−2z−17=0
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C
2x+y−z+1=0
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D
x−2y+z+1=0
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Solution
The correct option is C2x+y−z+1=0 Normal of p1=[2−31] Normal of p2=[1−11] If planes are perpendiculars then dot products of their normals must be 0, So consider normal of desired plane is [abc] Hence, 2a−3b+c=0 (Dot product with normal of p1) a−b+c=0 (Dot product with normal of p2) Solving above 2 we get , a−2b=0 So if we use normals of planes in option b & d, we notice that they don't satisfy the above equation We observe that option a does not pass through (-1, 3, 2) Since on substitution , 2.(−1)+3+2+1≠0