Two unit vectors ' a ^ 1 'and ' a ^ 2 ' are inclined to each other at an angle ' θ '. If ∣ a ^ 1 − a ^ 2 ∣ = 3 , then the value of ( a ^ 1 − a ^ 2 ) ⋅ ( 2 a

Question

Two unit vectors ' a ^ 1 ​ 'and ' a ^ 2 ​ ' are inclined to each other at an angle ' θ '. If ∣ a ^ 1 ​ − a ^ 2 ​ ∣ = 3 ​ , then the value of ( a ^ 1 ​ − a ^ 2 ​ ) ⋅ ( 2 a ^ 1 ​ − a ^ 2 ​ ) is

TestHub · Accepted Answer

∣ a ^ 1 ​ − a ^ 2 ​ ∣ = 3 ​ → ( 1 ) ∣ a ^ 1 ​ ∣ = ∣ a ^ 2 ​ ∣ = 1 a ^ 1 2 ​ + a ^ 2 2 ​ − 2 a ^ 1 ​ a ^ 2 ​ cos θ = 3 squaring (1) 1 + 1 − 2 cos θ = 3 = ( a ^ 1 ​ − a ^ 2 ​ ) ⋅ ( 2 a ^ 1 ​ − a ^ 2 ​ ) cos θ = − 1/2

Physics - Vectors Question with Solution | TestHub

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