Vector Algebra
Triple Products
Grade 12
Question:
<p>If <strong>a</strong> × (<strong>b</strong> × <strong>c</strong>) = <strong>0</strong>, then</p>
<p>(a) |<strong>a</strong>| = |<strong>b</strong>| · |<strong>c</strong>| = 1</p>
<p>(b) <strong>b</strong> ∥ <strong>c</strong></p>
<p>(c) <strong>a</strong> ∥ <strong>b</strong></p>
<p>(d) <strong>b</strong> ⊥ <strong>c</strong></p>
Step-by-Step Solution
Key Concept: Apply the scalar triple product expansion and analyze when the resulting expression equals zero.
Using a × ( b × c ) = ( a · c ) b − ( a · b ) c = 0 , we get ( a · c ) b = ( a · b ) c . This means b and c are parallel.
Correct Answer: B