Ex 10.3, 5 - Show unit vector: 1/7 (2i + 3j + 6k), 1/7(3-6j+2k) - 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, 5 Show that each of the given three vectors is a unit vector: 1﷮7﷯ (2 𝑖﷯ + 3 𝑗﷯ + 6 𝑘﷯), 1﷮7﷯ (3 𝑖﷯ – 6 𝑗﷯ + 2 𝑘﷯), 1﷮7﷯ (6 𝑖﷯ + 2 𝑗﷯ – 3 𝑘﷯), Also, show that they are mutually perpendicular to each other. 𝑎﷯ = 1﷮7﷯ (2 𝑖﷯ + 3 𝑗﷯ + 6 𝑘﷯) = 2﷮7﷯ 𝑖﷯ + 3﷮7﷯ 𝑗﷯ + 6﷮7﷯ 𝑘﷯ 𝑏﷯ = 1﷮7﷯ (3 𝑖﷯ − 6 𝑗﷯ + 2 𝑘﷯) = 3﷮7﷯ 𝑖﷯ – 6﷮7﷯ 𝑗﷯ + 2𝑘﷮7﷯ 𝑘﷯ 𝑐﷯ = 1﷮7﷯ (6 𝑖﷯ + 2 𝑗﷯ - 3 𝑘﷯) = 6﷮7﷯ 𝑖﷯ + 2﷮7﷯ 𝑗﷯ – 3﷮7﷯ 𝑘﷯ Magnitude of 𝑎﷯ = ﷮ 2﷮7﷯﷯﷮2﷯+ 3﷮7﷯﷯﷮2﷯+ 6﷮7﷯﷯﷮2﷯﷯ 𝑎﷯﷯ = ﷮ 4﷮49﷯+ 9﷮49﷯+ 36﷮49﷯﷯ = ﷮ 49﷮49﷯﷯ = 1 Since 𝑎﷯﷯ = 1 So, 𝑎﷯ is a unit vector. Magnitude of 𝑏﷯ = ﷮ 3﷮7﷯﷯﷮2﷯+ −6﷮7﷯﷯﷮2﷯+ 2﷮7﷯﷯﷮2﷯﷯ 𝑏﷯﷯ = ﷮ 9﷮49﷯+ 36﷮49﷯+ 4﷮49﷯﷯= ﷮ 49﷮49﷯﷯ = 1 Since 𝑏﷯﷯ = 1 So, 𝑏﷯ is a unit vector. Magnitude of 𝑐﷯ = ﷮ 6﷮7﷯﷯﷮2﷯+ 2﷮7﷯﷯﷮2﷯+ −3﷮7﷯﷯﷮2﷯﷯ 𝑐﷯﷯ = ﷮ 36﷮49﷯+ 4﷮49﷯+ 9﷮49﷯﷯ = ﷮ 49﷮49﷯﷯ = 1 Since 𝑐﷯﷯ = 1, So, 𝑐﷯ is a unit vector Now, we need to show that they are mutually perpendicular to each other. So, 𝒂﷯. 𝒃﷯ = 𝒃﷯. 𝒄﷯ = 𝒄﷯ . 𝒂﷯ = 0 Thus, they are mutually perpendiculars to each other.

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