Ex 10.2, 9 - Chapter 10 Class 12 Vector Algebra

Transcript

Ex 10.2, 9 For given vectors, 𝑎﷯ = 2 𝑖﷯ − 𝑗﷯ + 2 𝑘﷯ and 𝑏﷯ = − 𝑖﷯ + 𝑗﷯ − 𝑘﷯ , find the unit vector in the direction of the vector 𝑎﷯ + 𝑏﷯ 𝑎﷯ = 2 𝑖﷯ − j﷯ + 2 𝑘﷯ = 2 𝑖﷯ – 1 𝑗﷯ + 2 𝑘﷯ 𝑏﷯ = − 𝑖﷯ + 𝑗﷯ – 𝑘﷯ = −1 𝑖﷯ + 1 𝑗﷯ – 1 𝑘﷯ Now, ( 𝑎﷯ + 𝑏﷯) = (2 – 1) 𝑖﷯ + (-1 + 1) 𝑗﷯ + (2 – 1) 𝑘﷯ = 1 𝑖﷯ + 0 𝑗﷯ + 1 𝑘﷯ Let 𝑐﷯ = 𝑎﷯ + 𝑏﷯ ∴ c﷯ = 1 𝑖﷯ + 0 𝑗﷯ + 1 𝑘﷯ Magnitude of 𝑐﷯ = ﷮12+02+12﷯ 𝑐﷯﷯ = ﷮1+0+1﷯ = ﷮2﷯ Unit vector in direction of 𝑐﷯ = 1﷮ 𝑐﷯﷯﷯ . 𝑐﷯ 𝑐﷯ = 1﷮ ﷮2﷯﷯ 1 𝑖﷯+0 𝑗﷯+1 𝑘﷯﷯ 𝑐﷯ = 1﷮ ﷮2﷯﷯ 𝑖﷯ + 0 𝑗﷯ + 1﷮ ﷮2﷯﷯ 𝑘﷯ 𝑐﷯ = 𝟏﷮ ﷮𝟐﷯﷯ 𝒊﷯ + 𝟏﷮ ﷮𝟐﷯﷯ 𝒌﷯ Thus, unit vector in direction of 𝑐﷯ = 1﷮ ﷮2﷯﷯ 𝑖﷯ + 1﷮ ﷮2﷯﷯ 𝑘﷯