Vector Algebra
Division of Line Segment
Grade 12

Question:

<p><strong>Ex. 53</strong> In parallelogram ABCD, M is a point on DC which divides DC in the ratio 1 : 2 and AM intersects BD at Q. Point Q divides DB 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: Apply collinearity and section formula using position vectors to determine where line AM intersects diagonal BD.
Solution: Using similar vector analysis, when M divides DC in ratio 1:2 and AM intersects BD at Q, the point Q divides DB in the ratio 1:3. Thus, \(DQ = \frac{1}{4}DB\) and \(PB = \frac{1}{4}DB\).
Correct Answer: B

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