Ex 10.3, 3

Transcript

Ex 10.3, 3 Find the projection of the vector 𝑖﷯ − 𝑗﷯ on the vector 𝑖﷯ + 𝑗﷯ . Let 𝑎﷯ = 𝑖﷯ − 𝑗﷯ = 1 𝑖﷯ – 1 𝑗﷯ + 0 𝑘﷯ 𝑏﷯ = 𝑖﷯ + 𝑗﷯ = 1 𝑖﷯ + 1 𝑗﷯ + 0 𝑘﷯ Projector of vector 𝒂﷯ on 𝒃﷯ = 𝟏﷮ 𝒃﷯﷯﷯ ( 𝒂﷯ . 𝒃﷯) Now, 𝒂﷯ . 𝒃﷯ = (1 × 1) (−1 × 1) + (0 × 0) = 1 + (−1) + 0 = 0 Also, Magnitude of 𝑏﷯ = ﷮12+12+02﷯ 𝑏﷯﷯ = ﷮1+1+0﷯ = ﷮2﷯ Projection of 𝑎﷯ on 𝑏﷯ = 1﷮ 𝑏﷯﷯﷯ ( 𝑎﷯ . 𝑏﷯) = 1﷮ ﷮2﷯﷯ (0) = 0