CUET · MATHS · PYQ PAPER 2025
A unit vector perpendicular to the vectors \(\hat{i}-\hat{j}\) and \(\hat{i}+\hat{j}\) is
- A \(\hat{k}\)
- B \(-\left(\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right)\)
- C \(\frac{\hat{i}-\hat{j}}{\sqrt{2}}\)
- D \(\frac{\hat{i}+\hat{j}}{\sqrt{2}}\)
Answer & Solution
Correct Answer
(A) \(\hat{k}\)
Step-by-step Solution
Detailed explanation
\(\vec{n} = (\hat{i} - \hat{j}) \times (\hat{i} + \hat{j})\) \(= \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & -1 & 0 \\ 1 & 1 & 0 \end{vmatrix}\) \(= \hat{k}(1 \cdot 1 - (-1) \cdot 1) = 2\hat{k}\)…
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