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Physics · MOTION IN A PLANE

हिन्दी

Which of the following represents the unit vector \( \hat{n} \) in the direction of vector \( \mathbf{A} = 6\hat{i} + 8\hat{j} \)?

  1. \( 0.8\hat{i} + 0.6\hat{j} \)
  2. \( 6\hat{i} + 8\hat{j} \)
  3. \( 0.6\hat{i} + 0.8\hat{j} \)
  4. \( \frac{3}{5}\hat{i} - \frac{4}{5}\hat{j} \)

Correct answer · Option 3

\( 0.6\hat{i} + 0.8\hat{j} \)

Explanation

\( |\mathbf{A}| = \sqrt{6^2 + 8^2} = 10 \). Thus, \( \hat{n} = \frac{\mathbf{A}}{|\mathbf{A}|} = \frac{6\hat{i} + 8\hat{j}}{10} = 0.6\hat{i} + 0.8\hat{j} \).
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