Ex 10.3, 4 - Find projection of i + 3j + 7k on 7i - j + 8k - Ex 10.3

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Ex 10.3, 4 Find the projection of the vector 𝑖﷯ + 3 𝑗﷯ + 7 𝑘﷯ on the vector 7 𝑖﷯ - 𝑗﷯ + 8 𝑘﷯ . Projection of vector 𝒂﷯ on 𝒃﷯ = 𝟏﷮ 𝒃﷯﷯﷯ ( 𝒂﷯. 𝒃﷯) Let 𝑎﷯ = 1 𝑖﷯ + 3 𝑗﷯ + 7 𝑘﷯ 𝑏﷯ = 7 𝑖﷯ – 1 𝑗﷯ + 8 𝑘﷯ ( 𝒂﷯ . 𝒃﷯) = (1 × 7) + (3 × −1) + (7 × 8) = 7 + (−3) + 56 = 60 Magnitude of 𝑏﷯ = ﷮72+ −1﷯2+82﷯ 𝑏﷯﷯ = ﷮49+1+64﷯ = ﷮𝟏𝟏𝟒﷯ Projection of 𝑎﷯ on 𝑏﷯ = 1﷮ 𝑏﷯﷯﷯ ( 𝑎﷯. 𝑏﷯) = 1﷮ ﷮114﷯﷯ × 60 = 60﷮ ﷮114﷯﷯ Thus projection of 𝑎﷯ on 𝑏﷯ = 𝟔𝟎﷮ ﷮𝟏𝟏𝟒﷯﷯

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