MHT CET · Maths · Vector Algebra
\(\mathbf{i} \cdot(\mathbf{j} \times \mathbf{k})+\mathbf{j} \cdot(\mathbf{k} \times \mathbf{i})+\mathbf{k} \cdot(\mathbf{j} \times \mathbf{i})\) is equal to
- A 3
- B 2
- C 1
- D 0
Answer & Solution
Correct Answer
(C) 1
Step-by-step Solution
Detailed explanation
Given,
\(\begin{aligned} \mathbf{i} \cdot(\mathbf{j} \times \mathbf{k}) &+\mathbf{j} \cdot(\mathbf{k} \times \mathbf{i})+\mathbf{k} \cdot(\mathbf{j} \times \mathbf{i}) \\=& \mathbf{i} \cdot(\mathbf{i})+\mathbf{j} \cdot(\mathbf{j})+\mathbf{k} \cdot(-\mathbf{k}) \\=&(\mathbf{i} \cdot \mathbf{i})+(\mathbf{j} \cdot \mathbf{j})-(\mathbf{k} \cdot \mathbf{k}) \\=& 1+1-1=1 \end{aligned}\)
\(\begin{aligned} \mathbf{i} \cdot(\mathbf{j} \times \mathbf{k}) &+\mathbf{j} \cdot(\mathbf{k} \times \mathbf{i})+\mathbf{k} \cdot(\mathbf{j} \times \mathbf{i}) \\=& \mathbf{i} \cdot(\mathbf{i})+\mathbf{j} \cdot(\mathbf{j})+\mathbf{k} \cdot(-\mathbf{k}) \\=&(\mathbf{i} \cdot \mathbf{i})+(\mathbf{j} \cdot \mathbf{j})-(\mathbf{k} \cdot \mathbf{k}) \\=& 1+1-1=1 \end{aligned}\)
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