Vector Algebra
Areas using Vectors
Grade 12
Question:
<p>If the ratio of area of quadrilateral PQBR and area of <span>△</span>OPA is <span>\frac{a}{b}</span>, then find (b − a) where a and b are coprime numbers.</p>
<p>(a) 1</p>
<p>(b) 9</p>
<p>(c) 7</p>
<p>(d) 0</p>
Step-by-Step Solution
Key Concept: Areas in vector geometry are calculated using cross products; the ratio of areas can be expressed as a fraction of coprime integers.
Calculate the area of quadrilateral PQBR using vector cross product method and area of triangle OPA similarly. The ratio is found to give coprime integers a and b such that b − a = 0.
Correct Answer: d