Question

The plane x - 2y + 3z = 17 divides the line joining the points (-2, 4, 7) and (3, -5, 8) in the ratio

• A. 3:5
• B. 3:10
• C. 3:7
• D. none of these

Hint:

For plane dividing line, substitute general section point.

Answer 1

The Correct Option is C

Step 1: Use 3D section formula. Let ratio \(r= m:n\).
Step 2: Point coordinates of division: \[ x=\frac{–2n+3m}{m+n},\; y=\frac{4n–5m}{m+n},\; z=\frac{7n+8m}{m+n}. \]
Step 3: Substitute in plane equation and solve linear relation → gives 3:7. Hence → (C).