Question

Find the equation of the plane passing through the point (7, 8, 6) and parallel to the plane `bar"r"*(6hat"i" + 8hat"j" + 7hat"k")` = 0

Answer 1

The plane passes through the point A(7, 8, 6).

∴ x₁ = 7, y₁ = 8, z₁ = 6

Since the required plane is parallel to the plane `bar"r"*(6hat"i" + 8hat"j" + 7hat"k")` = 0

Direction ratios of normal vector will be a = 6, b = 8, c = 7.

Equation of a plane in Cartesian form is

a(x − x₁) + b(y − y₁) + c(z − z₁) = 0

∴ 6(x − 7) + 8(y − 8) + 7(z − 6) = 0

∴ 6x − 42 + 8y − 64 + 7z − 42 = 0

∴ 6x + 8y + 7z = 42 + 42 + 64

∴ 6x + 8y + 7z = 148