Question

For three non-coplanar vectors a, b and c, the expression a $\cdot$ (b $\times$ c) can be written as

• A. (a $\times$ b) $\cdot$ c
• B. (a $\times$ b) $\cdot$ (a $\times$ c)
• C. (a $\cdot$ b) $\times$ (a $\cdot$ c)
• D. (a $\cdot$ b) $\times$ c

Hint:

The scalar triple product \( a \cdot (b \times c) \) is invariant under cyclic permutations, meaning it can be written as \( (a \times b) \cdot c \).

Answer 1

The Correct Option is A

Step 1: Understanding the cross and dot products.
The expression a $\cdot$ (b $\times$ c) is a scalar triple product. The scalar triple product of three vectors is invariant under cyclic permutations, which means it can be written as (a $\times$ b) $\cdot$ c.
Step 2: Conclusion.
The correct answer is (A) (a $\times$ b) $\cdot$ c.