Question

The value of $[ \vec{i} + \vec{j}, \vec{j} + \vec{k}, \vec{k} + \vec{i} ]$ is:

• A. 2
• B. 1
• C. 0
• D. -2

Hint:

A useful identity: $[\vec{a}+\vec{b}, \vec{b}+\vec{c}, \vec{c}+\vec{a}] = 2[\vec{a}, \vec{b}, \vec{c}]$. Here $[\vec{i}, \vec{j}, \vec{k}] = 1$.

Answer 1

The Correct Option is A

Step 1: Concept
The scalar triple product $[ \vec{a}, \vec{b}, \vec{c} ]$ is the determinant of the components of the vectors.
Step 2: Analysis
The vectors are $(1, 1, 0), (0, 1, 1),$ and $(1, 0, 1)$.
Determinant $= \begin{vmatrix} 1 & 1 & 0
0 & 1 & 1
1 & 0 & 1 \end{vmatrix} = 1(1-0) - 1(0-1) + 0$.
Step 3: Conclusion
$= 1 + 1 = 2$.
Final Answer: (A)