Question

The equation of the plane containing the lines $2x - 5y + z = 3, x + y + \, z = 5$ and parallel to the plane $x + 3 y+ 6 z = 1$ is

• A. $2x + 6y + 12z = 13$
• B. $x + 3y + 6z = - 7$
• C. $x + 3y + 6z = 27$
• D. $2x + 6y + 12x = - 13$

Answer 1

Answer: (C)

$x + 3y + 6z = 27$

Answer 2

The correct option is(C): x +3 y +6 z =27.

The given lines are:

1. 2x - 5y + z = 3
2. x + y + z = 5

A(x − x 0​)+B(y − y 0​)+C(z − z 0​)=0,

where (A, B, C) is the direction vector of the plane, and (x_0, y_0, z_0) is a point on the plane.

Plugging in the values, we get:

1(x −3)+3(y +2)+6(z −4)=0,

which simplifies to:

x +3 y +6 z =27.

So, the equation of the plane containing the lines 2x - 5y + z = 3 and x + y + z = 5, and parallel to the plane x + 3y + 6z = 1, is

x +3 y +6 z =27.