Ex 10.3, 6 - Chapter 10 Class 12 Vector Algebra

Transcript

Ex 10.3, 6 Find 𝑎﷯﷯ and 𝑏﷯﷯, if ( 𝑎﷯ + b﷯) .( 𝑎﷯ – 𝑏﷯) = 8 and 𝑎﷯﷯ = 8 𝑏﷯﷯ ( 𝑎﷯ + b﷯) . ( 𝑎﷯ – 𝑏﷯) = 8 𝑎﷯.( 𝑎﷯ – b﷯) + 𝑏﷯.( 𝑎﷯ − 𝑏﷯) = 8 𝑎﷯. 𝑎﷯ − 𝑎﷯. 𝑏﷯ + 𝒃﷯. 𝒂﷯ − 𝑏﷯. 𝑏﷯ = 8 𝑎﷯. 𝑎﷯ − 𝑎﷯. 𝑏﷯ + 𝒂﷯. 𝒃﷯ − 𝑏﷯. 𝑏﷯ = 8 𝒂﷯. 𝒂﷯ − 𝒃﷯. 𝒃﷯ = 8 𝒂﷯﷯2 – 𝒃﷯﷯2 = 8 Also given that , 𝑎﷯﷯ = 8 𝑏﷯﷯ Putting this in (1), 𝒂﷯﷯2 – 𝑏﷯﷯2 = 8 (8 𝒃﷯﷯)2 − 𝑏﷯﷯2 = 8 64 𝑏﷯﷯2 − 𝑏﷯﷯2 = 8 63 𝑏﷯﷯2 = 8 𝑏﷯﷯2 = 8﷮63﷯ 𝑏﷯﷯ = ﷮8﷯﷮ ﷮63﷯﷯ ∴ 𝒃﷯﷯ = 𝟐 ﷮𝟐﷯﷮𝟑 ﷮𝟕﷯﷯ Also, 𝑎﷯﷯ = 8 × 𝑏﷯﷯ 𝑎﷯﷯ = 8 × 2 ﷮2﷯﷮3 ﷮7﷯﷯ ∴ 𝒂﷯﷯ = 𝟏𝟔 ﷮𝟐﷯﷮𝟑 ﷮𝟕﷯﷯