Example 7 - Find a vector in direction of vector a = i - 2j - Unit vector

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Example 7 Find a vector in the direction of vector 𝑎﷯ = 𝑖﷯ − 2 𝑗﷯ that has magnitude 7 units. 𝑎﷯ = 𝑖﷯ – 2 𝑗﷯ = 1 𝑖﷯ – 2 𝑗﷯ + 0 𝑘﷯ Magnitude of 𝑎﷯ = ﷮12+(−2)2+02﷯ 𝑎﷯﷯ = ﷮1+4+0﷯ = ﷮5﷯ Unit vector in direction of 𝑎﷯ = 1﷮𝑚𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝑎﷯﷯ × 𝑎﷯ 𝑎﷯ = 1﷮ ﷮5﷯﷯ 1 𝑖﷯ + 2 𝑗﷯ + 0 𝑘﷯﷯ 𝑎﷯ = 1﷮ ﷮5﷯﷯ 𝑖﷯ − 2﷮ ﷮5﷯﷯ 𝑗﷯ + 0 𝑘﷯ 𝑎﷯ = 1﷮ ﷮5﷯﷯ 𝑖﷯ − 2﷮ ﷮5﷯﷯ 𝑗﷯ Thus, Vector having a magnitude 1 = 1﷮ ﷮5﷯﷯ 𝑖﷯ − 2﷮ ﷮5﷯﷯ 𝑗﷯ Vector having a magnitude 7 = 7 1﷮ ﷮5﷯﷯ 𝑖﷯ − 2﷮ ﷮5﷯﷯ 𝑗﷯ ﷯ = 7﷮ ﷮5﷯﷯ 𝑖﷯ − 14﷮ ﷮5﷯﷯ 𝑗﷯ Thus, required vector is 𝟕﷮ ﷮𝟓﷯﷯ 𝒊﷯ − 𝟏𝟒﷮ ﷮𝟓﷯﷯ 𝒋﷯

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