Ex 10.3, 7 - Evaluate product (3a - 5b).(2a + 7b) - Scalar product - Solving

  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Ex 10.3, 7 Evaluate the product (3 ๐‘Ž๏ทฏ โˆ’ 5 ๐‘๏ทฏ) โ‹… (2 ๐‘Ž๏ทฏ + 7 ๐‘๏ทฏ). (3 ๐‘Ž๏ทฏ โˆ’ 5 ๐‘๏ทฏ) โ‹… (2 ๐‘Ž๏ทฏ + 7 ๐‘๏ทฏ) = 3 ๐‘Ž๏ทฏ . 2 ๐‘Ž๏ทฏ + 3 ๐‘Ž๏ทฏ.7 ๐‘๏ทฏ โˆ’ 5 ๐‘๏ทฏ.2 ๐‘Ž๏ทฏ โˆ’ 5 ๐‘๏ทฏ. 7 ๐‘๏ทฏ = 6( ๐‘Ž๏ทฏ. ๐‘Ž๏ทฏ) + 21( ๐‘Ž๏ทฏ. ๐‘๏ทฏ) โˆ’ 10 ( ๐’ƒ๏ทฏ. ๐’‚๏ทฏ) โˆ’ 35 ( ๐‘๏ทฏ. ๐‘๏ทฏ) = 6( ๐‘Ž๏ทฏ. ๐‘Ž๏ทฏ) + 21( ๐‘Ž๏ทฏ. ๐‘๏ทฏ) โˆ’ 10 ( ๐’‚๏ทฏ. ๐’ƒ๏ทฏ) โˆ’ 35 ( ๐‘๏ทฏ. ๐‘๏ทฏ) = 6( ๐’‚๏ทฏ. ๐’‚๏ทฏ) + 11 ( ๐‘Ž๏ทฏ. ๐‘๏ทฏ) โˆ’35 ( ๐’ƒ๏ทฏ. ๐’ƒ๏ทฏ) = 6 ๐’‚๏ทฏ๏ทฏ2 + 11( ๐‘Ž๏ทฏ. ๐‘๏ทฏ) โˆ’ 35 ๐’ƒ๏ทฏ๏ทฏ2 Therefore, (3 ๐‘Ž๏ทฏ โˆ’ 5 ๐‘๏ทฏ) โ‹… (2 ๐‘Ž๏ทฏ + 7 ๐‘๏ทฏ) = 6 ๐’‚๏ทฏ๏ทฏ2 + 11 ( ๐’‚๏ทฏ. ๐’ƒ๏ทฏ) โˆ’ 35 ๐’ƒ๏ทฏ๏ทฏ2

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