The equation of the plane through the point (1, 2, 3) and parallel to the plane 4x + 5y − 3z = 7 is:
A
4x + 5y − 3z = 6
B
4x + 5y − 3z = 1
C
4x + 5y + 3z = 7
D
4x + 5y − 3z = 5
Correct Option:
D
Explanation
Parallel planes have the same normal vector, so the required plane has the form 4x + 5y − 3z = C. Using the point (1, 2, 3), C = 4(1) + 5(2) − 3(3) = 4 + 10 − 9 = 5. Hence the plane is 4x + 5y − 3z = 5.
