If bmatrix 2 & 1 & -1 -1 & 2 & 1 1 & -1 & 2 bmatrix bmatrix a b c bmatrix = bmatrix 4 0 -2 bmatrix then the distance of point P(a, b, c) from the plane 2x + y + 2z = 10 is

Step-by-step solution

The given matrix equation represents the following system of linear equations: 2a + b - c = 4 -a + 2b + c = 0 a - b + 2c = -2 Adding the first and second equations gives a + 3b = 4 . Adding the second and third equations gives b + 3c = -2 . Adding the first and third equations gives 3a + c = 2 . Solving these equations, we get a = 1 , b = 1 , and c = -1 . The point P(a, b, c) is P(1, 1, -1) . The perpendicular distance of the point P(1, 1, -1) from the plane 2x + y + 2z - 10 = 0 is given by: d = |2(1) + 1(1) + 2(-1