Example 16 - Find projection of vector a = 2i + 3j + 2k on b - Examples

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Example 16 Find the projection of the vector 𝑎﷯ = 2 𝑖﷯ + 3 𝑗﷯ + 2 𝑘﷯ on the vector 𝑏﷯ = 𝑖﷯ + 2 𝑗﷯ + 𝑘﷯. Projection of vector 𝒂﷯ on 𝒃﷯ = 𝟏﷮| 𝒃﷯|﷯ ( 𝑎﷯. 𝑏﷯) 𝑎﷯ = 2 𝑖﷯ + 3 𝑗﷯ + 2 𝑘﷯ 𝑏﷯ = 1 𝑖﷯ + 2 𝑗﷯ + 1 𝑘﷯ ( 𝒂﷯. 𝒃﷯) = (2 × 1) + (3 × 2) + (2 × 1) = 2 + 6 + 2 = 10 Magnitude of 𝑏﷯ = ﷮12+22+12﷯ 𝑏﷯﷯ = ﷮1+4+1﷯ = ﷮6﷯ Projection of vector 𝑎﷯ on 𝑏﷯ = 1﷮| 𝑏﷯|﷯ ( 𝑎﷯. 𝑏﷯) = 1﷮ ﷮6﷯﷯ (10) = 10﷮ ﷮6﷯﷯ = 10﷮ ﷮6﷯﷯ × ﷮6﷯﷮ ﷮6﷯﷯ = 10﷮6﷯ × ﷮6﷯ = 𝟓﷮𝟑﷯ ﷮𝟔﷯ Thus projection of 𝑎﷯ on 𝑏﷯ is 5﷮3﷯ ﷮6﷯

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