Find the equation of the planes parallel to the plane 6x - 3y + 2z +

1.	Find the equation of the planes parallel to the plane 6x - 3y + 2z + 9 = 0 and at a distance 5 from the origin.
Answer» Given the equation 6x - 3y + 2z + 9 = 0 ∴ Its parallel equation 6x - 3y + 2z + d = 0 Given that equation passes from origin to 5 cm ∴ 5 = (6(0) - 3(0) + 2(0) + d)/√(6² + 3² + 2²) d = 5√(36 + 9 + 4) d = 5√49 d = 5 x 7 = 35 ∴ 6x - 3y + 2z + 35 = 0

Find the equation of the planes parallel to the plane 6x - 3y + 2z + 9 = 0 and at a distance 5 from the origin.

Answer»

Given the equation

6x - 3y + 2z + 9 = 0

∴ Its parallel equation

6x - 3y + 2z + d = 0

Given that equation passes from origin to 5 cm

∴ 5 = (6(0) - 3(0) + 2(0) + d)/√(6² + 3² + 2²)

d = 5√(36 + 9 + 4)

d = 5√49

d = 5 x 7 = 35

∴ 6x - 3y + 2z + 35 = 0