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 \(\frac{AX}{XD}\) is</p>
<p>(a) 5/2</p>
<p>(b) 6</p>
<p>(c) 7/3</p>
<p>(d) 4</p>
Step-by-Step Solution
Key Concept: Apply vector geometry with the constraint that OA ∥ CB and OD ∥ AB to find where X lies on AD.
Using the vector equations from the pentagon configuration with the given parallel and ratio conditions, the position of point X can be determined. The ratio \(\frac{AX}{XD} = 6\).
Correct Answer: b