1.2.1.2.1. Prove the Cauchy-Schwarz Inequality1.2.2. Prove the Triangle Inequalitylà b|≤ lal|b||a + b ≤ lal + band give a geometrical interpretation of this inequality.1.2.3. Show that if a + b and a – b are orthogonal, then the vectors a and must have thesame length.

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Answered: 1.2. 1.2.1. Prove the Cauchy-Schwarz…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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70 P is a point on a straight line with position vector r = a + tb. Show that 7=a+2a-bt+ B² By completing the square, show that is a minimum for the point P for which t-a-b/B. Show that at this point OP is perpendicular to the line r= a + tb. (This proves the well-known result that the shortest distance from a point to a line is the length of the perpendicular from that point to the line.)
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70 P is a point on a straight line with position vector r = a + tb. Show that 7=a+2a-bt+ B² By completing the square, show that is a minimum for the point P for which t-a-b/B. Show that at this point OP is perpendicular to the line r= a + tb. (This proves the well-known result that the shortest distance from a point to a line is the length of the perpendicular from that point to the line.)
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1.2. 1.2.1. Prove the Cauchy-Schwarz Inequality 1.2.2. Prove the Triangle Inequality |ā.bl≤ lä||b| là +b ≤lal + lờ| and give a geometrical interpretation of this inequality. 1.2.3. Show that if a + b and a - b are orthogonal, then the vectors a and b must have the same length.