Question

Equation of a plane parallel to the plane \( 9x - 8y + 7z = 10 \) is:

• A. \( 9x - 8y - 7z = 5 \)
• B. \( 9x - 8y + 7z = 5 \)
• C. \( 9x + 8y + 7z = 5 \)
• D. \( 9x - y + 7z = 5 \)

Hint:

For parallel planes, the normal vectors are the same, but the constant term varies. Simply adjust the constant term while keeping the direction ratios the same.

Answer 1

The Correct Option is B

The equation of a plane parallel to another plane is obtained by keeping the same direction ratios for the normal vector, but changing the constant. Here, the normal vector of the given plane is \( (9, -8, 7) \). For a plane parallel to this one, we keep the same direction ratios but change the constant to get \( 9x - 8y + 7z = 5 \).