Vector Algebra
Vector Addition and Subtraction
Grade 12
Question:
<p>If <strong>a</strong> and <strong>b</strong> are the vectors determined by two adjacent sides of a regular hexagon, then vector <strong>EO</strong> is</p>
<p>(a) <strong>a</strong> + <strong>b</strong></p>
<p>(b) <strong>a</strong> - <strong>b</strong></p>
<p>(c) 2<strong>a</strong></p>
<p>(d) 2<strong>b</strong></p>
Step-by-Step Solution
Key Concept: Use the property of regular hexagons where adjacent sides are equal and make 120° angles. Trace the vector path from E to O by decomposing it into components parallel to the given vectors.
Sol. OABCDE is a regular hexagon. Let OA = a and AB = b . By the properties of a regular hexagon and vector addition, we can express EO in terms of a and b . Tracing the path from E to O using the hexagon's geometry, we find that EO = a - b . ∴ Answer is (b).
Correct Answer: B