NTA Abhyas JEE Main2020MathematicsVector AlgebraPractice

If r → ⋅ i ^ = 2 r → ⋅ j ^ = 4 r → ⋅ k ^ and | r → | = 84 , then the value of r → ⋅ 2 i ^ - 3 j ^ + k ^ may be

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Correct answer

D. 6

Step-by-step solution

r → ⋅ i ^ = 2 r → ⋅ j ^ = 4 r → ⋅ k ^ Let r → = x i ^ + y j ^ + z k → x = 2 y = 4 z | r → | = 84 ⇒ 4 z 2 + 2 z 2 + z 2 = 84 z = 2 ; y = 4 ; x = 8 r → = 8 i ^ + 4 j ^ + 2 k ^ r → ⋅ 2 i ^ - 3 j ^ + k ^ = 16 – 12 + 2 = 6

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