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Question

If the distance of the plane passing through the point P(1,1,1) and perpendicular to the line x13=y10=z14 from the origin is k5 then the value of k is

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Solution

Equation of the plane passing through (1,1,1) is given by, A(x1)+B(y1)+C(z1)=0(1)
Since the line is perpendicular to the plane (1)
3(x1)+0(y1)+4(z1)=03x+4z7=0
Hence, distance from (0,0,0) to the plane (1) is,
d=∣ ∣732+42∣ ∣=75
k=7

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