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Mathematics · JEE | VECTOR ALGEBRA
हिन्दीMatch List-I with List-II: List-I List-II A Area of parallelogram with adjacent sides \( \vec{a}, \vec{b} \) I \( \frac{1}{2}|\vec{a}\times\vec{b}| \) B Area of triangle with adjacent sides \( \vec{a}, \vec{b} \) II \( |\vec{a}\times\vec{b}| \) C Projection of \( \vec{a} \) on \( \vec{b} \) III \( \frac{\vec{a}\cdot\vec{b}}{|\vec{b}|} \) D Unit vector perpendicular to \( \vec{a} \) and \( \vec{b} \) IV \( \frac{\vec{a}\times\vec{b}}{|\vec{a}\times\vec{b}|} \) Choose the correct answer from the options given below:
Match List-I with List-II:
| List-I | List-II | ||
|---|---|---|---|
| A | Area of parallelogram with adjacent sides \( \vec{a}, \vec{b} \) | I | \( \frac{1}{2}|\vec{a}\times\vec{b}| \) |
| B | Area of triangle with adjacent sides \( \vec{a}, \vec{b} \) | II | \( |\vec{a}\times\vec{b}| \) |
| C | Projection of \( \vec{a} \) on \( \vec{b} \) | III | \( \frac{\vec{a}\cdot\vec{b}}{|\vec{b}|} \) |
| D | Unit vector perpendicular to \( \vec{a} \) and \( \vec{b} \) | IV | \( \frac{\vec{a}\times\vec{b}}{|\vec{a}\times\vec{b}|} \) |
Choose the correct answer from the options given below:
View Answer & Solution
Correct answer · Option B
A-(II), B-(I), C-(III), D-(IV)
Explanation
Match formulas directly: Parallelogram area is \( |\vec{a}\times\vec{b}| \), triangle area is \( \frac{1}{2}|\vec{a}\times\vec{b}| \), projection is \( \frac{\vec{a}\cdot\vec{b}}{|\vec{b}|} \), normal unit vector is \( \frac{\vec{a}\times\vec{b}}{|\vec{a}\times\vec{b}|} \).
