Question

The image of the point (3, 2, 1) in the plane $2x - y + 3z = 7$ is

• A. (1, 2, 3)
• B. (2, 3, 1)
• C. (3, 2, 1)
• D. (2, 1, 3)

Hint:

If a point satisfies the plane equation, its image in that plane is the point itself.

Answer 1

The Correct Option is C

Step 1: Check if point is on the plane
Substitute the point $(x_1, y_1, z_1) = (3, 2, 1)$ into the plane equation $2x - y + 3z - 7 = 0$.
$2(3) - (2) + 3(1) - 7 = 6 - 2 + 3 - 7 = 0$.
Step 2: Conclusion
Since the result is zero, the point lies exactly on the plane. The image of any point lying on a plane is the point itself. Therefore, the image is (3, 2, 1).
Final Answer: (c)