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Class 12
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Vector of magnitude 5 units and in the direction opposite to

2i + 3j βˆ’ 6kΒ  isΒ  ____________

Vector of magnitude 5 units and in direction opposite to  2i + 3j - 6k

Question 15 (OR 2nd Question) - CBSE Class 12 Sample Paper for 2020 Boards - Part 2


Transcript

Question 15 (OR 2nd Question) Vector of magnitude 5 units and in the direction opposite to 2𝑖 Μ‚ + 3𝑗 Μ‚ βˆ’ 6π‘˜ Μ‚ is ____________ Let π‘Ž βƒ— = 2𝑖 Μ‚ + 3𝑗 Μ‚ – 6π‘˜ Μ‚ Magnitude of π‘Ž βƒ— = √(22+32+(βˆ’6)2) |π‘Ž βƒ— | = √(4+9+36) = √49 = 7 Unit vector opposite to direction of π‘Ž βƒ— = –1 Γ— 1/|π‘Ž βƒ— | . π‘Ž βƒ— = (βˆ’1)/7 (2𝑖 Μ‚ + 3𝑗 Μ‚ – 6π‘˜ Μ‚) Thus, Vector with magnitude 1 opposite to π‘Ž βƒ— = (βˆ’1)/7 (2𝑖 Μ‚ + 3𝑗 Μ‚ – 6π‘˜ Μ‚) Vector with magnitude 5 opposite to π‘Ž βƒ— = (βˆ’5)/7 (2𝑖 Μ‚ + 3𝑗 Μ‚ – 6π‘˜ Μ‚) = 5/7 (–2𝑖 Μ‚ – 3𝑗 Μ‚ + 6π‘˜ Μ‚) Hence, the required vector is πŸ“/πŸ• (–2π’Š Μ‚ – 3𝒋 Μ‚ + 6π’Œ Μ‚)

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.