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Planes in 3D

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Question

The distance of the point  P(3,8,2) from the line 12(x1)=14(y3)=13(z2) measured parallel to the plane 3x+2y2z+15=0 is

Moderate
Solution

Let A=(2λ+1,4λ+3,3λ+2)
Let this point lie on the line such that AP is parallel to the plane AP¯ is perpendicular to normal to the plane.
AP(3i^+2j^2k^)

3.(2λ2)+2(4λ5)2(3λ)=0

λ=2
therefore, A is (5,11,8), P = (3, 8, 2) , AP = 7


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