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Ex 10.2, 9 - For a = 2i - j + 2k, b = -i + j - k, find unit - Addition(resultant) of vectors

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Ex 10.2, 9 For given vectors, 𝑎īˇ¯ = 2 𝑖īˇ¯ − 𝑗īˇ¯ + 2 𝑘īˇ¯ and 𝑏īˇ¯ = − 𝑖īˇ¯ + 𝑗īˇ¯ − 𝑘īˇ¯ , find the unit vector in the direction of the vector 𝑎īˇ¯ + 𝑏īˇ¯ 𝑎īˇ¯ = 2 𝑖īˇ¯ − jīˇ¯ + 2 𝑘īˇ¯ = 2 𝑖īˇ¯ – 1 𝑗īˇ¯ + 2 𝑘īˇ¯ 𝑏īˇ¯ = − 𝑖īˇ¯ + 𝑗īˇ¯ – 𝑘īˇ¯ = −1 𝑖īˇ¯ + 1 𝑗īˇ¯ – 1 𝑘īˇ¯ Now, ( 𝑎īˇ¯ + 𝑏īˇ¯) = (2 – 1) 𝑖īˇ¯ + (-1 + 1) 𝑗īˇ¯ + (2 – 1) 𝑘īˇ¯ = 1 𝑖īˇ¯ + 0 𝑗īˇ¯ + 1 𝑘īˇ¯ Let 𝑐īˇ¯ = 𝑎īˇ¯ + 𝑏īˇ¯ ∴ cīˇ¯ = 1 𝑖īˇ¯ + 0 𝑗īˇ¯ + 1 𝑘īˇ¯ Magnitude of 𝑐īˇ¯ = īˇŽ12+02+12īˇ¯ 𝑐īˇ¯īˇ¯ = īˇŽ1+0+1īˇ¯ = īˇŽ2īˇ¯ Unit vector in direction of 𝑐īˇ¯ = 1īˇŽ 𝑐īˇ¯īˇ¯īˇ¯ . 𝑐īˇ¯ 𝑐īˇ¯ = 1īˇŽ īˇŽ2īˇ¯īˇ¯ 1 𝑖īˇ¯+0 𝑗īˇ¯+1 𝑘īˇ¯īˇ¯ 𝑐īˇ¯ = 1īˇŽ īˇŽ2īˇ¯īˇ¯ 𝑖īˇ¯ + 0 𝑗īˇ¯ + 1īˇŽ īˇŽ2īˇ¯īˇ¯ 𝑘īˇ¯ 𝑐īˇ¯ = 𝟏īˇŽ īˇŽđŸīˇ¯īˇ¯ 𝒊īˇ¯ + 𝟏īˇŽ īˇŽđŸīˇ¯īˇ¯ 𝒌īˇ¯ Thus, unit vector in direction of 𝑐īˇ¯ = 1īˇŽ īˇŽ2īˇ¯īˇ¯ 𝑖īˇ¯ + 1īˇŽ īˇŽ2īˇ¯īˇ¯ 𝑘īˇ¯

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