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:
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:
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Use the linear combination of plane equations to find the plane passing through the intersection of two planes.
Updated On: Apr 27, 2026
- \( x + y + z = 6 \)
- \( x + y + z = 3 \)
- \( 3x + 2y + z = 1 \)
- \( x + y + z = 0 \)
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The Correct Option is D
Solution and Explanation
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 \( x + y + z = 0 \).
Step 2: Conclusion. Thus, the equation of the required plane is \( x + y + z = 0 \).
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