**Consider the function** \( F(x, y) = e^{-x^2/3 - y^2/3} \) **and the point** \( P(3, 3) \).**a.** Find the unit vectors that give the direction of steepest ascent and steepest descent at \( P \).**b.** Find a vector that points in a direction of no change in the function at \( P \).-----**a.** The direction of steepest ascent is \(( \, \, )\).

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Answered: -x²13-y²13 Consider the function F(x,y)…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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13. Given the points A(3,5) and B( – 3, – 7), find a. the vector equation of the line.
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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-x²13-y²13 Consider the function F(x,y) = e and the point P(3,3). a. Find the unit vectors that give the direction of steepest ascent and steepest descent at P. b. Find a vector that points in a direction of no change in the function at P. a. The direction of steepest ascent is