Ex 10.4, 7 - Show that a x (b + c) =  a x b + a x c - Ex 10.4

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Ex 10.4, 7 Let the vectors ๐‘Ž๏ทฏ ๐‘๏ทฏ, ๐‘๏ทฏ be given as ๐‘Ž๏ทฎ1๏ทฏ ๐‘–๏ทฏ + ๐‘Ž๏ทฎ2๏ทฏ ๐‘—๏ทฏ + ๐‘Ž๏ทฎ3๏ทฏ ๐‘˜๏ทฏ, ๐‘๏ทฎ1๏ทฏ ๐‘–๏ทฏ + ๐‘๏ทฎ2๏ทฏ ๐‘—๏ทฏ + ๐‘๏ทฎ3๏ทฏ ๐‘˜๏ทฏ, ๐‘๏ทฎ1๏ทฏ ๐‘–๏ทฏ + ๐‘๏ทฎ2๏ทฏ ๐‘—๏ทฏ + ๐‘๏ทฎ3๏ทฏ ๐‘˜๏ทฏ Then show that ๐‘Ž๏ทฏ ร— ( ๐‘๏ทฏ + ๐‘๏ทฏ) = ๐‘Ž๏ทฏ ร— ๐‘๏ทฏ + ๐‘Ž๏ทฏ ร— ๐‘๏ทฏ. Let ๐‘Ž๏ทฏ = ๐‘Ž๏ทฎ1๏ทฏ ๐‘–๏ทฏ + ๐‘Ž๏ทฎ2๏ทฏ ๐‘—๏ทฏ + ๐‘Ž๏ทฎ3๏ทฏ ๐‘˜๏ทฏ ๐‘๏ทฏ = ๐‘๏ทฎ1๏ทฏ ๐‘–๏ทฏ + ๐‘๏ทฎ2๏ทฏ ๐‘—๏ทฏ + ๐‘๏ทฎ3๏ทฏ ๐‘˜๏ทฏ, ๐‘๏ทฏ = ๐‘๏ทฎ1๏ทฏ ๐‘–๏ทฏ + ๐‘๏ทฎ2๏ทฏ ๐‘—๏ทฏ + ๐‘๏ทฎ3๏ทฏ ๐‘˜๏ทฏ We need to show : ๐‘Ž๏ทฏ ร— ( ๐‘๏ทฏ + ๐‘๏ทฏ) = ๐‘Ž๏ทฏ ร— ๐‘๏ทฏ + ๐‘Ž๏ทฏ ร— ๐‘๏ทฏ LHS ( ๐‘๏ทฏ + ๐‘๏ทฏ) = (๐‘1 + ๐‘1) ๐‘–๏ทฏ + (๐‘2 + ๐‘2) ๐‘—๏ทฏ + (๐‘3 + ๐‘3) ๐‘˜๏ทฏ ๐’‚๏ทฏ ร— ( ๐’ƒ๏ทฏ + ๐’„๏ทฏ) = ๐‘–๏ทฏ๏ทฎ ๐‘—๏ทฏ๏ทฎ ๐‘˜๏ทฏ๏ทฎ ๐‘Ž1๏ทฎ(๐‘1+๐‘1)๏ทฏ๏ทฎ ๐‘Ž2๏ทฎ(๐‘2+๐‘2)๏ทฏ๏ทฎ ๐‘Ž3๏ทฎ(๐‘3+๐‘3)๏ทฏ๏ทฏ๏ทฏ = ๐‘–๏ทฏ ๐‘Ž2ร—(๐‘3 + ๐‘3)โˆ’(๐‘2 + ๐‘2)ร—๐‘Ž3 ๏ทฏ โˆ’ ๐‘—๏ทฏ ๐‘Ž1ร—(๐‘3 + ๐‘3)โˆ’(๐‘1 + ๐‘1)ร—๐‘Ž3 ๏ทฏ + ๐‘˜๏ทฏ ๐‘Ž1ร—(๐‘2 + ๐‘2)โˆ’(๐‘1 + ๐‘1)ร—๐‘Ž2 ๏ทฏ = ๐‘Ž2๐‘3+๐‘Ž2๐‘3โˆ’ ๐‘๏ทฎ2๏ทฏ๐‘Ž3โˆ’๐‘2๐‘Ž3 ๏ทฏ ๐‘–๏ทฏ โˆ’ ๐‘Ž1 ๐‘3โˆ’๐‘1 ๐‘Ž3+๐‘Ž1 ๐‘3โˆ’๐‘1๐‘Ž3๏ทฏ ๐‘—๏ทฏ + ๐‘Ž1๐‘2+๐‘Ž1๐‘2โˆ’ ๐‘๏ทฏ1 ๐‘Ž๏ทฏ2โˆ’๐‘1๐‘Ž2 ๏ทฏ ๐‘˜๏ทฏ

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