WBJEE · Maths · Vector Algebra
For any vector \(\mathbf{x},\) where \(\hat{\mathbf{i}}, \hat{\mathbf{j}}, \hat{\mathbf{k}}\) have their usual meanings the value of \((\mathbf{x} \times \hat{\mathbf{i}})^{2}+(\mathbf{x} \times \mathbf{j})^{2}+(\mathbf{x} \times \mathbf{k})^{2}\) where \(\mathbf{i}, \mathbf{j}, \mathbf{k}\) have their usual meanings, is equal to
- A \(|\mathbf{x}|^{2}\)
- B \(2|\mathbf{x}|^{2}\)
- C \(3|\mathbf{x}|^{2}\)
- D \(4|\mathbf{x}|^{2}\)
Answer & Solution
Correct Answer
(B) \(2|\mathbf{x}|^{2}\)
Step-by-step Solution
Detailed explanation
Let \(\mathbf{x}=\alpha \mathbf{i}+\beta \mathbf{j}+\gamma \mathbf{k}\) Then, \(\mathbf{x} \times \mathbf{i}=-\beta \hat{\mathbf{k}}+\gamma \hat{\mathbf{j}}\)…
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