Find the vector equation of the plane passing through the point (a, b, b) and parallel to the plane There is a error in question …… the point should be (a,b,c) instead of (a,b,b) to get the required answer.

Question

Philoid · Accepted Answer

Formula : Plane = r . (n) = d

Where r = any random point

n = normal vector of plane

d = distance of plane from origin

If two planes are parallel , then their normal vectors are same.

Therefore ,

Parallel Plane r . (i + j + k) = 2

Normal vector = (i + j + k)

∴ Normal vector of required plane = (i + j + k)

Equation of required plane r . (i + j + k) = d

In cartesian form x + y + z = d

Plane passes through point (a,b,c) therefore it will satisfy it.

(a) + (b) + (c) = d

d = a + b + c

Equation of required plane r . (i + j + k) = a + b + c