Question

The Cartesian equation of a plane through A (7, 8, 6) and parallel to the XY plane is

Options

• z = 7

• z = 8

• z = 6

• z = 4

Answer 1

z = 6

Explanation:

The equation of plane through A(7, 8, 6) is

a(x − 7) + b(y − 8) + c(z − 6) = 0 ...(i)

Since the required plane is parallel to the XY plane

∴ Direction ratios are 0, 0, 1.

∴ The equation of a plane is

0(x − 7) + 0(y − 0) + 1(z − 6) = 0

⇒ z − 6 = 0

⇒ z = 6