CBSE Class 12 Sample Paper for 2020 Boards
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CBSE Class 12 Sample Paper for 2020 Boards
Last updated at Dec. 16, 2024 by Teachoo
Transcript
Question 15 (OR 2nd Question) Vector of magnitude 5 units and in the direction opposite to 2𝑖 ̂ + 3𝑗 ̂ − 6𝑘 ̂ is ____________ Let 𝑎 ⃗ = 2𝑖 ̂ + 3𝑗 ̂ – 6𝑘 ̂ Magnitude of 𝑎 ⃗ = √(22+32+(−6)2) |𝑎 ⃗ | = √(4+9+36) = √49 = 7 Unit vector opposite to direction of 𝑎 ⃗ = –1 × 1/|𝑎 ⃗ | . 𝑎 ⃗ = (−1)/7 (2𝑖 ̂ + 3𝑗 ̂ – 6𝑘 ̂) Thus, Vector with magnitude 1 opposite to 𝑎 ⃗ = (−1)/7 (2𝑖 ̂ + 3𝑗 ̂ – 6𝑘 ̂) Vector with magnitude 5 opposite to 𝑎 ⃗ = (−5)/7 (2𝑖 ̂ + 3𝑗 ̂ – 6𝑘 ̂) = 5/7 (–2𝑖 ̂ – 3𝑗 ̂ + 6𝑘 ̂) Hence, the required vector is 𝟓/𝟕 (–2𝒊 ̂ – 3𝒋 ̂ + 6𝒌 ̂)
