If a → and b → are vectors perpendicular to each other and a → = 2 , b → = 3 and c → × a → = b → , then the least value of c → - a → is

Question

If a → and b → are vectors perpendicular to each other and a → = 2 , b → = 3 and c → × a → = b → , then the least value of c → - a → is,

MARKS App · Accepted Answer

c → × a → = b → ⇒ c → a → sin ⁡ θ = 3 ⇒ c → sin ⁡ θ = 3 2 c → - a → 2 = c → 2 + a → 2 - 2 a → ⋅ c → = c → 2 + 4 - 2 a → c → cos ⁡ θ = c → 2 + 4 - 4 c → cos ⁡ θ = 9 4 c o s e c 2 θ + 4 - 6 cot ⁡ θ = 9 4 + 9 4 c o t 2 θ - 6 cot ⁡ θ + 4 ⇒ c - a 2 = 9 4 + 3 2 cot ⁡ θ - 2 2 ≥ 9 4 Hence, c → - a → ≥ 3 2

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