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Consider two vectors a → = 3 i ^ - 2 j ^ + 4 k ^ and b → = j ^ + 2 k ^ . If c → is a unit vector and k be the maximum value of a · b → × c → , then the value of k 2 - 50 is equal to

Correct answer

59

Step-by-step solution

a → × b → = i ^ j ^ k ^ 3 - 2 4 0 1 2 = i ^ - 8 - j ^ 6 + k ^ 3 = - 8 i ^ - 6 j ^ + 3 k ^ a → b → c → = a → × b → ⋅ c → ≤ a → × b → c → ⇒ maximum value of a → b → c → = a → × b → c → ⇒ k = 64 + 36 + 9 . 1 = 109 ⇒ k 2 - 50 = 109 - 50 = 59

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