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Co - ordinate Geometry 3D Geometry

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Equation of the plane passing through the points (0, 0, 1), (1, 0, 1) and (1, –1, 0) is

A. x+ y + z = 1

B. y + z = 1

C. y – z + 1 = 0

D. x + y = 1

E. None of the above

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Correct choice: C

Explanation:

Equation of a plane through the point (0, 0, 1) is
a(x – 0) + b(y – 0) + c(z –1) = 0
Or ax + by + cz – c = 0
Since it passes through (1, 0, 1) and (1, –1, 0) then
a = 0, a– b – c = 0
Solving a + 0b + 0c = 0
a – b – c = 0
By cross multiplication we have a/0 =b/+1 = c/-1
∴Reqd. equation is + y – z +1 = 0
or y – z +1 = 0

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Eamcet Mathematics Co - ordinate Geometry 3D Geometry

Eamcet Mathematics
Co - ordinate Geometry 3D Geometry