Supplementary Example 6
Last updated at May 29, 2018 by Teachoo
Last updated at May 29, 2018 by Teachoo
Transcript
Supplementary Example 6 For any three vectors ∴ 𝑎, 𝑏, and 𝑐, prove that 𝑎 + 𝑏 𝑏+ 𝑐 𝑐+ 𝑎 = 2 [ 𝑎 , 𝑏, 𝑐] To prove 𝑎 + 𝑏 𝑏+ 𝑐 𝑐+ 𝑎 = 2 [ 𝑎 , 𝑏, 𝑐] Solving LHS 𝑎 + 𝑏 𝑏+ 𝑐 𝑐+ 𝑎 = ( 𝑎 + 𝑏). ( 𝑏+ 𝑐) × ( 𝑐+ 𝑎) = ( 𝑎 + 𝑏). ( 𝑏× 𝑐) + ( 𝑏× 𝑎)+( 𝒄× 𝒄) + ( 𝑐× 𝑎) = ( 𝑎+ 𝑏). 𝑏× 𝑐) + ( 𝑏× 𝑎 + 0 + ( 𝑐 × 𝑎) = 𝑎. ( 𝑏 × 𝑐) + 𝑏.( 𝑏 × 𝑐) + 𝑎. ( 𝑏 × 𝑎) + 𝑏.( 𝑏 × 𝑎) + 𝑎.( 𝑐 × 𝑎) + 𝑏.( 𝑐 × 𝑎) = 𝑎, 𝑏, 𝑐 + 𝒃, 𝒃, 𝒄 + 𝒂, 𝒃, 𝒂 + 𝒃, 𝒃, 𝒂 + 𝒂, 𝒄, 𝒂 + 𝑏, 𝑐, 𝑎 = 𝑎, 𝑏, 𝑐 + 0 + 0 + 0 + 0 + 𝑏, 𝑐, 𝑎 = 𝑎, 𝑏, 𝑐 + 𝒃, 𝒄, 𝒂 = 𝑎, 𝑏, 𝑐 + 𝒂, 𝒃, 𝒄 = 2 𝑎, 𝑏, 𝑐 = R.H.S Hence proved
Supplementary examples and questions from CBSE
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Supplementary examples and questions from CBSE
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