Find the equation of the plane that passes through X-axis and point (3

1.	Find the equation of the plane that passes through X-axis and point (3,2, 4).
Answer» Equation of plane passing through (3, 2, 4) a (x – 3) + b(y – 2) + c(z – 4) = 0 …..(1) ∵ Plane passes through X-axis ∴ a = 0,d = 0 ⇒ by + cz = 0 …..(2) From (1), a = 0 so b (y – 2) + c(z – 4) = 0 …..(3) ⇒ by – 2b + cz – 4c = 0 ⇒ by + cz – 2b – 4c = 0 ⇒ – 2b = c [∵ by + cz = 0 from (2)] ⇒ b = -2c ∴ Equation of plane passing through (3,2,4) and X-axis b(y- 2) + c(z – 4) = 0 ⇒ – 2c(y – 2) + c(z – 4) = 0 ⇒ -2y + 4 + z – 4 = 0 ⇒ 2y – z = 0

Find the equation of the plane that passes through X-axis and point (3,2, 4).

Answer»

Equation of plane passing through (3, 2, 4)

a (x – 3) + b(y – 2) + c(z – 4) = 0 …..(1)

∵ Plane passes through X-axis

∴ a = 0,d = 0 ⇒ by + cz = 0 …..(2)

From (1), a = 0 so b (y – 2) + c(z – 4) = 0 …..(3)

⇒ by – 2b + cz – 4c = 0

⇒ by + cz – 2b – 4c = 0

⇒ – 2b = c [∵ by + cz = 0 from (2)]

⇒ b = -2c

∴ Equation of plane passing through (3,2,4) and X-axis b(y- 2) + c(z – 4) = 0

⇒ – 2c(y – 2) + c(z – 4) = 0

⇒ -2y + 4 + z – 4 = 0

⇒ 2y – z = 0