Home > Vector Algebra > None > 01873b18-b10e-576b-a31e-9b6318f839e2

Vector Algebra

Vector Addition and Geometry

Grade 12

Question:

<p>Consider the regular hexagon ABCDEF with centre at O (origin). Find \(\vec{AD} + \vec{EB} + \vec{FC}\)</p>

<p>(a) \(2\vec{AB}\)</p>

<p>(b) \(3\vec{AB}\)</p>

<p>(c) \(4\vec{AB}\)</p>

<p>(d) None of these</p>

Step-by-Step Solution

Key Concept: Exploit the symmetry of the regular hexagon and express each vector in terms of the fundamental vector AB.

In a regular hexagon ABCDEF with centre O, using symmetry properties and vector addition, we find that \(\vec{AD} + \vec{EB} + \vec{FC} = 3\vec{AB}\).

Correct Answer: b