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Physics · MOTION IN A PLANE
हिन्दीMatch List-I with List-II: List-I List-II A Magnitude of vector \( \mathbf{A} \) in 3D space I \( \frac{\mathbf{A}}{|\mathbf{A}|} \) B Direction cosine with z-axis (\( \cos\gamma \)) II \( \sqrt{A_x^2 + A_y^2 + A_z^2} \) C Unit vector along vector \( \mathbf{A} \) III \( \frac{A_z}{\sqrt{A_x^2 + A_y^2 + A_z^2}} \) D Property of zero vector \( \mathbf{0} \) IV \( 0 \cdot \mathbf{A} = \mathbf{0} \) Choose the correct answer from the options given below:
Match List-I with List-II:
| List-I | List-II | ||
|---|---|---|---|
| A | Magnitude of vector \( \mathbf{A} \) in 3D space | I | \( \frac{\mathbf{A}}{|\mathbf{A}|} \) |
| B | Direction cosine with z-axis (\( \cos\gamma \)) | II | \( \sqrt{A_x^2 + A_y^2 + A_z^2} \) |
| C | Unit vector along vector \( \mathbf{A} \) | III | \( \frac{A_z}{\sqrt{A_x^2 + A_y^2 + A_z^2}} \) |
| D | Property of zero vector \( \mathbf{0} \) | IV | \( 0 \cdot \mathbf{A} = \mathbf{0} \) |
Choose the correct answer from the options given below:
View Answer & Solution
Correct answer · Option A
A-II, B-III, C-I, D-IV
Explanation
The magnitude of a 3D vector is \( \sqrt{A_x^2+A_y^2+A_z^2} \), its direction cosine along the z-axis is \( A_z/|A| \), a unit vector in its direction is \( \mathbf{A}/|\mathbf{A}| \), and scalar multiplication of zero with any vector gives the zero vector \( \mathbf{0} \).
