Question

An equation of the plane passing through the line of intersection of the planes \( x + y + z = 6 \) and \( 2x + 3y + 4z = 5 \), and passing through \( (1, 1, 1) \) is:

• A. \( x + y + z = 6 \)
• B. \( x + y + z = 3 \)
• C. \( 3x + 2y + z = 1 \)
• D. \( x + y + z = 0 \)

Hint:

Use the linear combination of plane equations to find the plane passing through the intersection of two planes.

Answer 1

The Correct Option is D

Step 1: Use the method of linear combination. To find the equation of the plane passing through the line of intersection of two planes, we use a linear combination of the given planes' equations, ensuring that the point \( (1, 1, 1) \) lies on the plane.
Step 2: Conclusion. Thus, the equation of the required plane is \( x + y + z = 0 \).