Vector Algebra
Section Formula and Ratios
Grade 12
Question:
<p>Let OABCD be a pentagon in which the sides OA and CB are parallel and the sides OD and AB are parallel. Also, OA : CB = 2 : 1 and OD : AB = 1 : 3. The ratio \(\frac{OX}{XC}\) is</p>
<p>(a) 3/4</p>
<p>(b) 1/3</p>
<p>(c) 2/5</p>
<p>(d) 1/2</p>
Step-by-Step Solution
Key Concept: Use the parallelism conditions and given ratios to find the position vector of X, then compute the required ratio.
Using vector properties and the given parallel conditions with ratios OA : CB = 2 : 1 and OD : AB = 1 : 3, we can express the position of point X in terms of the vertices. The ratio \(\frac{OX}{XC} = \frac{3}{4}\).
Correct Answer: a