Example 8 - Find unit vector in direction of sum of vectors - Addition(resultant) of vectors

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Example 8 Find the unit vector in the direction of the sum of the vectors, 𝑎﷯ = 2 𝑖﷯ + 2 𝑗﷯ – 5 𝑘﷯ and 𝑏﷯ = 2 𝑖﷯ + 𝑗﷯ + 3 𝑘﷯ 𝑎﷯ = 2 𝑖﷯ + 2 𝑗﷯ – 5 𝑘﷯ 𝑏﷯ = 2 𝑖﷯ + 1 𝑗﷯ + 3 𝑘﷯ ( 𝑎﷯ + 𝑏﷯) = (2 + 2) 𝑖﷯ + (2 + 1) 𝑗﷯ + (–5 + 3) 𝑘﷯ = 4 𝑖﷯ + 3 𝑗﷯ – 2 𝑘﷯ Let 𝑐﷯ = ( 𝑎﷯ + 𝑏﷯) ∴ 𝑐﷯ = 4 𝑖﷯ + 3 𝑗﷯ – 2 𝑘﷯ Magnitude of 𝑐﷯ = ﷮42+32+ −2﷯2﷯ 𝑐﷯﷯ = ﷮16+9+4﷯ = ﷮29﷯ Unit vector in direction of 𝑐﷯ = 1﷮ 𝑐﷯﷯﷯ 𝑐﷯ 𝑐﷯ = 1﷮ ﷮29﷯﷯ 4 𝑖﷯ + 3 𝑗﷯ − 2 𝑘﷯﷯ 𝑐﷯ = 4﷮ ﷮29﷯﷯ 𝑖﷯ + 3﷮ ﷮29﷯﷯ 𝑗﷯ – 2﷮ ﷮29﷯﷯ 𝑘﷯ Thus, required unit vector = 𝟒﷮ ﷮𝟐𝟗﷯﷯ 𝒊﷯ + 𝟑﷮ ﷮𝟐𝟗﷯﷯ 𝒋﷯ – 𝟐﷮ ﷮𝟐𝟗﷯﷯ 𝒌﷯

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