Misc 7 - Find unit vector parallel to vector 2a - b + 3c - Miscellaneous

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Misc 7 If 𝑎﷯ = 𝑖﷯ + 𝑗﷯ + 𝑘﷯, 𝑏﷯ = 2 𝑖﷯ − 𝑗﷯ + 3 𝑘﷯ and 𝑐﷯ = 𝑖﷯ − 2 𝑗﷯ + 𝑘﷯ , find a unit vector parallel to the vector 2 𝑎﷯ – 𝑏﷯ + 3 𝑐﷯ . 𝑎﷯ = 𝑖﷯ + 𝑗﷯ + 𝑘﷯ = 1 𝑖﷯ −1 𝑗﷯ + 1 𝑘﷯ 𝑏﷯ = 2 𝑖﷯ + 𝑗﷯ + 3 𝑘﷯ = 2 𝑖﷯ −1 𝑗﷯ + 3 𝑘﷯ 𝑐﷯ = 𝑖﷯ − 2 𝑗﷯ + 𝑘﷯ = 1 𝑖﷯ −2 𝑗﷯ + 1 𝑘﷯ Let 𝑟﷯ = 2 𝑎﷯ − 𝑏﷯ + 3 𝑐﷯ = 2(1 𝑖﷯ −2 𝑗﷯ + 1 𝑘﷯) − (2 𝑖﷯ − 1 𝑗﷯ + 3 𝑘﷯) + 3(1 𝑖﷯ −2 𝑗﷯ + 1 𝑘﷯) = 2 𝑖﷯ − 1 𝑗﷯ + 2 𝑘﷯ − 2 𝑖﷯ − 1 𝑗﷯ + 3 𝑘﷯ + 3 𝑖﷯ − 6 𝑗﷯ + 3 𝑘﷯ = (2 − 2 + 3) 𝑖﷯ + (2 + 1 − 6) 𝑗﷯ + (2 − 3 + 3) 𝑘﷯ = 3 𝑖﷯ – 3 𝑗﷯ + 2 𝑘﷯ ∴ 𝒓﷯ = 3 𝒊﷯ – 3 𝒋﷯ + 2 𝒌﷯ Magnitude of 𝑟﷯ = ﷮32+ −3﷯2+22﷯ 𝑟﷯﷯ = ﷮9+9+4﷯ = ﷮22﷯ Unit vector in the direction of 𝑟﷯ = 1﷮ 𝑟﷯﷯﷯ x 𝑟﷯ = 1﷮ ﷮22﷯﷯ × 3 𝑖﷯ −3 𝑗﷯+2 𝑘﷯﷯ = 3﷮ ﷮22﷯﷯ 𝑖﷯ – 3﷮ ﷮22﷯﷯ 𝑗﷯ + 2﷮ ﷮22﷯﷯ 𝑘﷯ Hence the required vector is 𝟑﷮ ﷮𝟐𝟐﷯﷯ 𝒊﷯ – 𝟑﷮ ﷮𝟐𝟐﷯﷯ 𝒋﷯ + 𝟐﷮ ﷮𝟐𝟐﷯﷯ 𝒌﷯

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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