Question

Let \( \vec{b} = 3i - 2j + k \) and \( \vec{c} = i - j - k \) be two vectors. If \( \vec{a} \) is a vector such that \( \vec{a} + \vec{b} + \vec{c} = 0 \), then \( | \vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a} | \) is:

• A. 15
• B. \( \sqrt{261} \)
• C. \( \sqrt{234} \)
• D. 33

Hint:

For problems involving cross products and vector sums, use vector identities to simplify and evaluate the expression.

Answer 1

The Correct Option is C

We are given the condition \( \vec{a} + \vec{b} + \vec{c} = 0 \). By using this and applying the properties of the cross product, we compute \( | \vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a} | \), which simplifies to \( \sqrt{234} \).