Vector Algebra
Scalar Triple Product
Grade 12
Question:
<p>If <span style='text-decoration: overline;'>AB</span> <span style='text-decoration: overline;'>AC</span> <span style='text-decoration: overline;'>AB</span> × <span style='text-decoration: overline;'>AC</span> = <span style='text-decoration: overline;'>λ</span> <span style='text-decoration: overline;'>AE</span> <span style='text-decoration: overline;'>AG</span> <span style='text-decoration: overline;'>AE</span> × <span style='text-decoration: overline;'>AG</span>, then the value of <span style='text-decoration: overline;'>λ</span> is:</p>
<p>(a) –18</p>
<p>(b) 18</p>
<p>(c) –324</p>
<p>(d) 324</p>
Step-by-Step Solution
Key Concept: Scalar triple product relationships between two sets of vectors determine the proportionality constant λ.
Using scalar triple product properties and vector relationships, the value of λ is determined to be 324.
Correct Answer: d