Question

If the scalar triple product of three vectors \( \vec{a}, \vec{b}, \vec{c} \) is given as \([\vec{a}\ \vec{b}\ \vec{c}] = 3\), then find the value of the scalar triple product of their cross products, denoted as \([ \vec{a} \times \vec{b} \quad \vec{b} \times \vec{c} \quad \vec{c} \times \vec{a} ]\).

• A. 3
• B. 6
• C. 9
• D. 27

Hint:

Memorize the identity: \[ [\vec{a} \times \vec{b}\ \vec{b} \times \vec{c}\ \vec{c} \times \vec{a}] = [\vec{a}\ \vec{b}\ \vec{c}]^2 \] It saves a lot of time in competitive exams.

Answer 1

The Correct Option is C