Ex 10.2, 10 - Find a vector in direction of 5i - j + 2k - Unit vector

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Ex 10.2, 10 Find a vector in the direction of vector 5 𝑖﷯ − 𝑗﷯ + 2 𝑘﷯ which has magnitude 8 units. 𝑎﷯ = 5 𝑖﷯ − 𝑗﷯ + 2 𝑘﷯ = 5 𝑖﷯ − 1 𝑗﷯ + 2 𝑘﷯ Magnitude of 𝑎﷯ = ﷮52+ −1﷯2+22﷯ 𝑎﷯﷯ = ﷮25+1+4﷯ = ﷮30﷯ Unit vector in direction of 𝑎﷯ = 1﷮ 𝑎﷯﷯﷯ . 𝑎﷯ 𝑎﷯ = 1﷮ ﷮30﷯﷯ . 5 𝑖﷯−1 𝑗﷯+2 𝑘﷯﷯ 𝑎﷯ = 5﷮ ﷮30﷯﷯ 𝑖﷯ − 1﷮ ﷮30﷯﷯ 𝑗﷯ + 2﷮ ﷮30﷯﷯ 𝑘﷯ Thus, unit vector 𝑎﷯ = 5﷮ ﷮30﷯﷯ 𝑖﷯ − 1﷮ ﷮30﷯﷯ 𝑗﷯ + 2﷮ ﷮30﷯﷯ 𝑘﷯ Vector with magnitude 1 = 5﷮ ﷮30﷯﷯ 𝑖﷯ − 1﷮ ﷮30﷯﷯ 𝑗﷯ + 2﷮ ﷮30﷯﷯ 𝑘﷯ Vector with magnitude 8 = 8 5﷮ ﷮30﷯﷯ 𝑖﷯ − 1﷮ ﷮30﷯﷯ 𝑗﷯ + 2﷮ ﷮30﷯﷯ 𝑘﷯﷯ = 𝟒𝟎﷮ ﷮𝟑𝟎﷯﷯ 𝒊﷯ – 𝟖﷮ ﷮𝟑𝟎﷯﷯ 𝒋﷯ + 𝟏𝟔﷮ ﷮𝟑𝟎﷯﷯ 𝒌﷯ Hence, the required vector is 40﷮ ﷮30﷯﷯ 𝑖﷯ – 8﷮ ﷮30﷯﷯ 𝑗﷯ + 16﷮ ﷮30﷯﷯ 𝑘﷯

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