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Physics · MOTION IN A PLANE
हिन्दीMatch List-I with List-II: List-I List-II A Magnitude of 2D vector \( \mathbf{A} = A_x \hat{i} + A_y \hat{j} \) I \( \tan^{-1}(\frac{A_y}{A_x}) \) B Unit vector \( \hat{n} \) in direction of \( \mathbf{A} \) II \( \sqrt{A_x^2 + A_y^2 + A_z^2} \) C Direction angle \( \theta \) with x-axis in 2D III \( \sqrt{A_x^2 + A_y^2} \) D Magnitude of 3D vector \( \mathbf{A} = A_x \hat{i} + A_y \hat{j} + A_z \hat{k} \) IV \( \frac{\mathbf{A}}{|\mathbf{A}|} \) Choose the correct answer from the options given below:
Match List-I with List-II:
| List-I | List-II | ||
|---|---|---|---|
| A | Magnitude of 2D vector \( \mathbf{A} = A_x \hat{i} + A_y \hat{j} \) | I | \( \tan^{-1}(\frac{A_y}{A_x}) \) |
| B | Unit vector \( \hat{n} \) in direction of \( \mathbf{A} \) | II | \( \sqrt{A_x^2 + A_y^2 + A_z^2} \) |
| C | Direction angle \( \theta \) with x-axis in 2D | III | \( \sqrt{A_x^2 + A_y^2} \) |
| D | Magnitude of 3D vector \( \mathbf{A} = A_x \hat{i} + A_y \hat{j} + A_z \hat{k} \) | IV | \( \frac{\mathbf{A}}{|\mathbf{A}|} \) |
Choose the correct answer from the options given below:
Correct answer · Option 2
A-(III), B-(IV), C-(I), D-(II)
Explanation
In 2D, \( |\mathbf{A}| = \sqrt{A_x^2 + A_y^2} \) and \( \tan\theta = A_y / A_x \). A unit vector is defined as \( \mathbf{A} / |\mathbf{A}| \), and in 3D, \( |\mathbf{A}| = \sqrt{A_x^2 + A_y^2 + A_z^2} \).
