Vector Algebra
Vector Conditions and Triple Products
Grade 12
Question:
<p>Let <strong>a</strong> = \(2\mathbf{i} + \mathbf{j} - 2\mathbf{k}\) and <strong>b</strong> = \(\mathbf{i} + \mathbf{j}\). If <strong>c</strong> is a vector such that \(\mathbf{a} \cdot \mathbf{c} = |\mathbf{c}|\), \(|\mathbf{c} - \mathbf{a}| = 2\sqrt{2}\) and the angle between \(\mathbf{a} \times \mathbf{b}\) and <strong>c</strong> is 30°, then \(|(\mathbf{a} \times \mathbf{b}) \times \mathbf{c}|\) is equal to</p>
<p>(a) \(\frac{2}{3}\)</p>
<p>(b) \(\frac{3}{2}\)</p>
Step-by-Step Solution
Key Concept: Apply the conditions on the dot product, magnitude, and angle to determine the vector c, then compute the vector triple product.
This is an incomplete problem statement in the source material (only two options are provided and no complete solution is shown).
Correct Answer: B