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Question

Let a plane P pass through the point (3,7,7) and contain the line, x23=y32=z+21. If distance of the plane P from the origin is d, then d2 is equal to

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Solution

Equation of plane through the point (3,7,7) and containing the line x23=y32=z+21 is
∣ ∣x2y3z+232737+2321∣ ∣=0
∣ ∣x2y3z+2145321∣ ∣=0
x+y+z3=0
Now, distance of the plane from origin is
d=∣ ∣312+12+12∣ ∣
d2=3

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