Find the equation of the plane with intercept 3 on the y-axis and para

1.	Find the equation of the plane with intercept 3 on the y-axis and parallel to ZOX plane.
Answer» Equation of ZOX plane is y = 0 Direction ratio of normal to this plane is (0,1,0) since the required plane is parallel to y = 0 Direction ratio of its normal is also (0,1,0). Intercepts on y-axis is 3, ∴ The point (0, 3, 0) lies on the plane. ∴ equation of plane (x – 0) + 1 (y – 3) + 0 (z – 0) = 0 ∴ y = 3.

Find the equation of the plane with intercept 3 on the y-axis and parallel to ZOX plane.

Answer»

Equation of ZOX plane is y = 0

Direction ratio of normal to this plane is (0,1,0)

since the required plane is parallel to y = 0

Direction ratio of its normal is also (0,1,0). Intercepts on y-axis is 3,

∴ The point (0, 3, 0) lies on the plane.

∴ equation of plane

(x – 0) + 1 (y – 3) + 0 (z – 0) = 0

∴ y = 3.