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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Example 31 (Supplementary NCERT) Prove that [๐‘Žย โƒ—, ๐‘ย โƒ—, ๐‘ย โƒ—+๐‘‘ย โƒ— ] = [๐‘Žย โƒ—, ๐‘ย โƒ—, ๐‘ย โƒ— ] + [๐‘Žย โƒ—, ๐‘ย โƒ—, ๐‘‘ย โƒ— ] To prove [๐‘Žย โƒ—, ๐‘ย โƒ—, ๐‘ย โƒ—+๐‘‘ย โƒ— ] = [๐‘Žย โƒ—, ๐‘ย โƒ—, ๐‘ย โƒ— ] + [๐‘Žย โƒ—, ๐‘ย โƒ—, ๐‘‘ย โƒ— ] Solving LHS [๐‘Žย โƒ—, ๐‘ย โƒ—, ๐‘ย โƒ—+๐‘‘ย โƒ— ] = ๐‘Žย โƒ— . ["(" ๐‘ย โƒ—") " ร— "(" ๐‘ย โƒ—+๐‘‘ย โƒ—)] = ๐‘Žย โƒ— .["(" ๐‘ย โƒ—ร—๐‘ย โƒ—") + (" ๐‘ย โƒ—ร—๐‘‘ย โƒ—) ] = ๐‘Žย โƒ— .["(" ๐‘ย โƒ—ร—๐‘ย โƒ—")" ] + ๐‘Žย โƒ— .["(" ๐‘ย โƒ—ร—๐‘‘ย โƒ—)] = [๐‘Žย โƒ—", " ๐‘ย โƒ—", " ๐‘ย โƒ— ] + [๐’‚ย โƒ—", " ๐’ƒย โƒ—", " ๐’…ย โƒ— ] = RHS Hence proved Example 31 (Supplementary NCERT) Prove that [๐‘Žย โƒ—, ๐‘ย โƒ—, ๐‘ย โƒ—+๐‘‘ย โƒ— ] = [๐‘Žย โƒ—, ๐‘ย โƒ—, ๐‘ย โƒ— ] + [๐‘Žย โƒ—, ๐‘ย โƒ—, ๐‘‘ย โƒ— ] To prove [๐‘Žย โƒ—, ๐‘ย โƒ—, ๐‘ย โƒ—+๐‘‘ย โƒ— ] = [๐‘Žย โƒ—, ๐‘ย โƒ—, ๐‘ย โƒ— ] + [๐‘Žย โƒ—, ๐‘ย โƒ—, ๐‘‘ย โƒ— ] Solving LHS [๐‘Žย โƒ—, ๐‘ย โƒ—, ๐‘ย โƒ—+๐‘‘ย โƒ— ] = ๐‘Žย โƒ— . ["(" ๐‘ย โƒ—") " ร— "(" ๐‘ย โƒ—+๐‘‘ย โƒ—)] = ๐‘Žย โƒ— .["(" ๐‘ย โƒ—ร—๐‘ย โƒ—") + (" ๐‘ย โƒ—ร—๐‘‘ย โƒ—) ] = ๐‘Žย โƒ— .["(" ๐‘ย โƒ—ร—๐‘ย โƒ—")" ] + ๐‘Žย โƒ— .["(" ๐‘ย โƒ—ร—๐‘‘ย โƒ—)] = [๐‘Žย โƒ—", " ๐‘ย โƒ—", " ๐‘ย โƒ— ] + [๐’‚ย โƒ—", " ๐’ƒย โƒ—", " ๐’…ย โƒ— ] = RHS Hence proved Example 31 (Supplementary NCERT) Prove that [๐‘Žย โƒ—, ๐‘ย โƒ—, ๐‘ย โƒ—+๐‘‘ย โƒ— ] = [๐‘Žย โƒ—, ๐‘ย โƒ—, ๐‘ย โƒ— ] + [๐‘Žย โƒ—, ๐‘ย โƒ—, ๐‘‘ย โƒ— ] To prove [๐‘Žย โƒ—, ๐‘ย โƒ—, ๐‘ย โƒ—+๐‘‘ย โƒ— ] = [๐‘Žย โƒ—, ๐‘ย โƒ—, ๐‘ย โƒ— ] + [๐‘Žย โƒ—, ๐‘ย โƒ—, ๐‘‘ย โƒ— ] Solving LHS [๐‘Žย โƒ—, ๐‘ย โƒ—, ๐‘ย โƒ—+๐‘‘ย โƒ— ] = ๐‘Žย โƒ— . ["(" ๐‘ย โƒ—") " ร— "(" ๐‘ย โƒ—+๐‘‘ย โƒ—)] = ๐‘Žย โƒ— .["(" ๐‘ย โƒ—ร—๐‘ย โƒ—") + (" ๐‘ย โƒ—ร—๐‘‘ย โƒ—) ] = ๐‘Žย โƒ— .["(" ๐‘ย โƒ—ร—๐‘ย โƒ—")" ] + ๐‘Žย โƒ— .["(" ๐‘ย โƒ—ร—๐‘‘ย โƒ—)] = [๐‘Žย โƒ—", " ๐‘ย โƒ—", " ๐‘ย โƒ— ] + [๐’‚ย โƒ—", " ๐’ƒย โƒ—", " ๐’…ย โƒ— ] = RHS Hence proved

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