CUET · MATHS · PYQ PAPER 2025
If \(\vec{a}\) is any vector, then \(|\vec{a} \times \hat{i}|^2+|\vec{a} \times \hat{j}|^2+|\vec{a} \times \hat{k}|^2\) is equal to
- A \(|\vec{a}|^2\)
- B \(2|\vec{a}|^2\)
- C \(3|\vec{a}|^2\)
- D \(4|\vec{a}|^2\)
Answer & Solution
Correct Answer
(B) \(2|\vec{a}|^2\)
Step-by-step Solution
Detailed explanation
\(| \vec{a} \times \hat{i} |^2 = |\vec{a}|^2 |\hat{i}|^2 - (\vec{a} \cdot \hat{i})^2 = |\vec{a}|^2 - a_x^2\) \(| \vec{a} \times \hat{j} |^2 = |\vec{a}|^2 - a_y^2\) \(| \vec{a} \times \hat{k} |^2 = |\vec{a}|^2 - a_z^2\)…
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