Explanation Given: Let e and f are unit vectors such that ‖ e + f ‖ = 3 2 . Formula used: Distributive law: ( u + v ) ⋅ w = u ⋅ w + v ⋅ w Scalar multiple law: u ⋅ ( a v ) = a ( u ⋅ v ) Commutative law: u ⋅ v = v ⋅ u The dot product of v and w is v ⋅ w = ‖ v ‖ ‖ w ‖ cos θ . Calculation: Let e and f are unit vectors such that ‖ e + f ‖ = 3 2 . ‖ e + f ‖ = 3 2 … (1) Take square on both sides. ‖ e + f ‖ 2 = ( 3 2 ) 2 Simplify the above equation. ‖ e ‖ 2 + ‖ f ‖ 2 + 2 e ⋅ f = 3 2 Since, e and f are unit vectors. So, ‖ e ‖ = 1 and ‖ f ‖ = 1 . ‖ e ‖ 2 + ‖ f ‖ 2 + 2 e ⋅ f = 3 2 ( 1 ) 2 + ( 1 ) 2 + 2 e ⋅ f = 3 2 2 e ⋅ f = 3 2 − 2 2 e ⋅ f = − 1 2 e ⋅ f = − 1 4 Now, consider ‖ 2 e − 3 f ‖ Take square on ‖ 2 e − 3 f ‖ ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 13.3, Problem 48E

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If $e and f$ are unit vectors such that $‖ e + f ‖ = \sqrt{\frac{3}{2}}$ , then find $‖ 2 e - 3 f ‖$ .

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Chapter 13.3, Problem 47E

Chapter 13.3, Problem 49E

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Ch. 13.1 - Prob. 1PQ Ch. 13.1 - Prob. 2PQ Ch. 13.1 - Prob. 3PQ Ch. 13.1 - Prob. 4PQ Ch. 13.1 - Prob. 5PQ Ch. 13.1 - Prob. 6PQ Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E

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If e and f are unit vectors such that ‖ e + f ‖ = 3 2 , then find ‖ 2 e − 3 f ‖ .

Solution Summary: The author explains that if e and f are unit vectors, then the value of 2 is 4.

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Chapter 13 Solutions

If e and f are unit vectors such that ‖ e + f ‖ = 3 2 , then find ‖ 2 e − 3 f ‖ .

Solution Summary: The author explains that if e and f are unit vectors, then the value of 2 is 4.

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Chapter 13 Solutions

If $e and f$ are unit vectors such that $‖ e + f ‖ = \sqrt{\frac{3}{2}}$ , then find $‖ 2 e - 3 f ‖$ .