Explanation Given information: The Cauchy-Schwarz inequality is given as, | v ⋅ w | ≤ ‖ v ‖ ‖ w ‖ Formula used: The following formula is used. ‖ v × w ‖ 2 = ‖ v ‖ 2 ‖ w ‖ 2 − ( v ⋅ w ) 2 Proof: Always the magnitude of a vector is greater than or equal zero.Therefore, 0 ≤ ‖ v × w ‖ 2 . 0 ≤ ‖ v × w ‖ 2 0 ≤ ‖ v ‖ 2 ‖ w ‖ 2 − ( v ⋅ w ) 2 ( v ⋅ w ) 2 ≤ ‖ v ‖ 2 ‖ w ‖ 2 ( v ⋅ w ) 2 ≤ ‖ v ‖ 2 ‖ w ‖ 2 | v ⋅ w | ≤ ‖ v ‖ ‖ w ‖ Therefore, it is clear that ‖ v × w ‖ 2 is less than or equal ‖ v ‖ 2 ‖ w ‖ 2 . | v ⋅ w | ≤ ‖ v ‖ ‖ w ‖ Suppose that v = k w where k is an arbitrary natural number, then the angle θ between v and w is zero

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Chapter 13.4, Problem 74E

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To prove:The Cauchy-Schwarz inequality and if and only if w is a multiple of v or, v or w is zero then,

|v⋅w|=‖v‖‖w‖

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Chapter 13.4, Problem 73E

Chapter 13.4, Problem 75E

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الاسم يمنع استخدام الآلة الحاسبة ظلل في ورقة الإجابة الدائرة التي تحتوي على الحرف (ص) للإجابة الصحيحة والحرف (خ) للإجابة الخطأ بحسب رقم الفقرة لكل مما يأتي: درجة لكل فقرة. ( ) نها جا 元 جتا = صفر س ۱ س س -۱ ( ) يمكن إعادة تعريف الدالة د(س) = س قاس لكي تكون متصلة عند س = 7 ( ) إذا كانت د(س) = (٢) س - س ) ؛ فإن د(١) = ٦ ٢ س ص ( ) إذا كانت س + 0= ؛ فإن عند ) - ١ ، - ٦ ) تساوي (٦) ( ) إذا كانت د(س) = س ه ، و (س) = ٣ س ٢ + ٢ س ؛ فإن ( د ) (۱) = ۸ ) ( معادلة ناظم الدالة ص = د(س) عند النقطة ) ( ، د (۲)) هي ص - (د (م) - - د (۲) ( س - م ) ( ) إذا كانت ص = ظتا٢ س ؛ فإن ص = ٢ ص قتا ٢س ) ( إذا كانت د(س) = س ؛ فإن د (T) = جتاس 1- T ( ) إذا كانت د(س) = 1 - جناس جاس ؛ فإن د () = - 1 ( ) إذا كانت الدالة د (س) تحقق شروط مبرهنة القيمة المتوسطة على [ ، ب ] ، فإنه يوجد جـ ] ، ب [ بحيث (جـ) = (P) + (~)- - ب + P 1 2 3 4 5 6 7 8 9 10 11 ( ) للدالة د(س) = لو ( س ) + (٣) نقطة حرجة عند س = . ( ) إذا كان س = - ٢ مقارباً رأسياً للدالة د(س) 12 10 13 14 15 16 17 س = لو|س | + ث - = ۲ س + ٣ ب س + ٤ ، فإن معادلة…

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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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To prove: The Cauchy-Schwarz inequality and if and only if w is a multiple of v or, v or w is zero then, | v ⋅ w | = ‖ v ‖ ‖ w ‖

Solution Summary: The author explains how the Cauchy-Schwarz inequality is proved if the magnitude of a vector is greater than or equal zero.

Videos

To prove:The Cauchy-Schwarz inequality and if and only if w is a multiple of v or, v or w is zero then,

|v⋅w|=‖v‖‖w‖

Want to see the full answer?

Chapter 13 Solutions

To prove: The Cauchy-Schwarz inequality and if and only if w is a multiple of v or, v or w is zero then, | v ⋅ w | = ‖ v ‖ ‖ w ‖

Solution Summary: The author explains how the Cauchy-Schwarz inequality is proved if the magnitude of a vector is greater than or equal zero.

Videos

To prove:The Cauchy-Schwarz inequality and if and only if w is a multiple of v or, v or w is zero then, |v⋅w|=‖v‖‖w‖

Want to see the full answer?

Chapter 13 Solutions

To prove:The Cauchy-Schwarz inequality and if and only if w is a multiple of v or, v or w is zero then,

|v⋅w|=‖v‖‖w‖