Vector Algebra
Division of Line Segment
Grade 12
Question:
<p><strong>Ex. 52</strong> In parallelogram ABCD, L is a point on BC which divides BC in the ratio 1 : 2. AL intersects BD at P. Point P divides AL in the ratio</p>
<p>(a) 1 : 2</p>
<p>(b) 1 : 3</p>
<p>(c) 3 : 1</p>
<p>(d) 2 : 1</p>
Step-by-Step Solution
Key Concept: Use position vectors and collinearity conditions to find the division ratio of intersection point P on line AL.
Solution: Using vector methods and properties of parallelograms, when L divides BC in ratio 1:2 and AL intersects BD at P, the point P divides AL in the ratio 3:1.
Correct Answer: C