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Example 18 - lf a is a unit vector (x - a) . (x + a) = 8, find x

Example 18 - Chapter 10 Class 12 Vector Algebra - Part 2

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Example 18 If π‘Ž βƒ— is a unit vector and (π‘₯ βƒ— βˆ’ π‘Ž βƒ—) β‹… (π‘₯ βƒ— + π‘Ž βƒ—) = 8 , then find |π‘₯ βƒ—| Given π‘Ž βƒ— is a unit vector So, π‘Ž βƒ— has a magnitude 1. ∴ |𝒂 βƒ— | = 1. Given that (𝒙 βƒ— βˆ’ 𝒂 βƒ—) β‹… (𝒙 βƒ— + 𝒂 βƒ—) = 8 π‘₯ βƒ— . π‘₯ βƒ— + π‘₯ βƒ— . π‘Ž βƒ— βˆ’ 𝒂 βƒ— . 𝒙 βƒ— βˆ’ π‘Ž βƒ— . π‘Ž βƒ— = 8 π‘₯ βƒ— . π‘₯ βƒ— + π‘₯ βƒ— . π‘Ž βƒ— βˆ’ 𝒙 βƒ— . 𝒂 βƒ— βˆ’ π‘Ž βƒ— . π‘Ž βƒ— = 8 𝒙 βƒ— . 𝒙 βƒ— βˆ’ 𝒂 βƒ— . 𝒂 βƒ— = 8 |𝒙 βƒ— |2 βˆ’ |𝒂 βƒ— |2 = 8 |π‘₯ βƒ— |2 βˆ’ 12 = 8 (Using: π‘₯ βƒ— . π‘Ž βƒ— = π‘Ž βƒ— . π‘₯ βƒ— ) |π‘₯ βƒ— |2 = 8 + 1 |π‘₯ βƒ— |2 = 9 |π‘₯ βƒ— | = Β± √9 |π‘₯ βƒ— | = Β± 3 Since magnitude is not negative, ∴ |𝒙 βƒ— | = 3

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