Short Answer TypeFind equation of the plane parallel to x + 3y – 2z + 7 = 0 and passing through the origin.
The equation of any plane through (a, b, c) is
A (x – a) + B (y – b) + C (z – c) = 0 ...(1)
Consider the plane
∴ normal to the plane is the vector 
∴ normal to the plane has direction ratios 1, 1, 1.
∴ A = k, B = k, C = k
Putting values of A, B. C in (1), we get,
k (x – a) + k (y – b) + k (z – c) = 0
or x – a + y – b + z – c = 0
or x + y + z – a –b – c = 0
which is required equation of plane.
Long Answer TypeShort Answer TypeIn each of the following cases, determine the direction cosines of the normal to the plane and the distance from the origin.
z = 2
In each of the following cases, determine the direction cosines of the normal to the plane and the distance from the origin.
x + y + z = 1
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