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Ex 10.3, 10 - If a, b, c are such, a + b is perpendicular to c - Ex 10.3

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Ex 10.3, 10 If ๐‘Ž๏ทฏ = 2 ๐‘–๏ทฏ + 2 ๐‘—๏ทฏ + 3 ๐‘˜๏ทฏ, ๐‘๏ทฏ = โˆ’ ๐‘–๏ทฏ + 2 ๐‘—๏ทฏ + ๐‘˜๏ทฏ and ๐‘๏ทฏ = 3 ๐‘–๏ทฏ + ๐‘—๏ทฏ are such that ๐‘Ž๏ทฏ +๐œ† ๐‘๏ทฏ is perpendicular to ๐‘๏ทฏ , then find the value of ๐œ†. ๐‘Ž๏ทฏ = 2 ๐‘–๏ทฏ + 2 ๐‘—๏ทฏ + 3 ๐‘˜๏ทฏ ๐‘๏ทฏ = โˆ’ ๐‘–๏ทฏ + 2 ๐‘—๏ทฏ + ๐‘˜๏ทฏ = โˆ’1 ๐‘–๏ทฏ + 2 ๐‘—๏ทฏ + 1 ๐‘˜๏ทฏ ๐‘๏ทฏ = 3 ๐‘–๏ทฏ + ๐‘—๏ทฏ = 3 ๐‘–๏ทฏ + 1 ๐‘—๏ทฏ + 0 ๐‘˜๏ทฏ ( ๐‘Ž๏ทฏ + ๐œ† ๐‘๏ทฏ) = (2 ๐‘–๏ทฏ + 2 ๐‘—๏ทฏ + 3 ๐‘˜๏ทฏ) + ๐œ† (-1 ๐‘–๏ทฏ + 2 ๐‘—๏ทฏ + 1 ๐‘˜๏ทฏ) = 2 ๐‘–๏ทฏ + 2 ๐‘—๏ทฏ + 3 ๐‘˜๏ทฏ โˆ’ ๐œ† ๐‘–๏ทฏ + 2๐œ† ๐‘—๏ทฏ + ๐œ† ๐‘˜๏ทฏ = (2 โˆ’ ๐œ†) ๐‘–๏ทฏ + (2 + 2๐œ†) ๐‘—๏ทฏ + (3 + ๐œ†) ๐‘˜๏ทฏ If ( ๐‘Ž๏ทฏ + ๐œ† ๐‘๏ทฏ) is perpendicular to ๐‘๏ทฏ ( ๐‘Ž๏ทฏ + ๐œ† ๐‘๏ทฏ). ๐‘๏ทฏ = 0 2โˆ’๐œ†๏ทฏ ๐‘–๏ทฏ+ 2+2๐œ†๏ทฏ ๐‘—๏ทฏ+(3+๐œ†) ๐‘˜๏ทฏ๏ทฏ . (3 ๐‘–๏ทฏ + 1 ๐‘—๏ทฏ + 0 ๐‘˜๏ทฏ) = 0 (2 - ๐œ†).3 + (2 + 2๐œ†).1 + (3 + ๐œ† ).0 = 0 3.2 โˆ’ 3๐œ† + 2 + 2๐œ† + 0 = 0 6 โ€“ 3๐œ† + 2 + 2๐œ† = 0 8 โˆ’ ๐œ† = 0 ๐œ† = 8 โˆด ๐œ† = 8

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