Ex 10.4, 4 - Show that (a - b) x (a + b) = 2(a x b) - Ex 10.4

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  1. Chapter 10 Class 12 Vector Algebra
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Ex 10.4, 4 Show that ( ๐‘Ž๏ทฏ โˆ’ ๐‘๏ทฏ) ร— ( ๐‘Ž๏ทฏ + ๐‘๏ทฏ) = 2( ๐‘Ž๏ทฏ ร— ๐‘๏ทฏ) Solving L.H.S ( ๐‘Ž๏ทฏ โˆ’ ๐‘๏ทฏ) ร— ( ๐‘Ž๏ทฏ + ๐‘๏ทฏ) = ๐‘Ž๏ทฏ ร— ( ๐‘Ž๏ทฏ + ๐‘๏ทฏ) โˆ’ ๐‘๏ทฏ ร— ( ๐‘Ž๏ทฏ + ๐‘๏ทฏ) = ๐‘Ž๏ทฏ ร— ๐‘Ž๏ทฏ + ๐‘Ž๏ทฏ ร— ๐‘๏ทฏ โˆ’ ๐’ƒ๏ทฏ ร— ๐’‚๏ทฏ โˆ’ ๐‘๏ทฏ ร— ๐‘๏ทฏ = ๐‘Ž๏ทฏ ร— ๐‘Ž๏ทฏ + ๐‘Ž๏ทฏ ร— ๐‘๏ทฏ โˆ’ (โˆ’ ๐’‚๏ทฏ ร— ๐’ƒ๏ทฏ) โˆ’ ๐‘๏ทฏ ร— ๐‘๏ทฏ = ๐‘Ž๏ทฏ ร— ๐‘Ž๏ทฏ + ๐‘Ž๏ทฏ ร— ๐‘๏ทฏ + ๐‘Ž๏ทฏ ร— ๐‘๏ทฏ โˆ’ ๐‘๏ทฏ ร— ๐‘๏ทฏ = ๐’‚๏ทฏ ร— ๐’‚๏ทฏ + 2( ๐‘Ž๏ทฏ ร— ๐‘๏ทฏ) โˆ’ ๐’ƒ๏ทฏ ร— ๐’ƒ๏ทฏ = 0 + 2( ๐‘Ž๏ทฏ ร— ๐‘๏ทฏ) โˆ’ 0 = 2 ( ๐‘Ž๏ทฏ ร— ๐‘๏ทฏ) = RHS Since LHS = RHS, Hence proved.

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