Question

The ratio in which the join of (2, 1, 5) and (3, 4, 3) is divided by the plane x + y − z = 12 is:

• A. 3:5
• B. 5:7
• C. 1:3
• D. 4:5

Hint:

Use section parameter t for line–plane intersection problems.

Answer 1

The Correct Option is B

Parametric point on the join: (2+t,1+3t,5-2t) Substitute in plane equation: (2+t)+(1+3t)-(5-2t)=\tfrac12 ⟹ 6t-2=\tfrac12 ⟹ t=(5)/(12) Hence, AP:PB=(5)/(12):(7)/(12)=5:7