3. Let f(,y) = cos(xy) and a =(,1). (a) Find f(a). (b) Find a unit vector which is normal to the level set {(x,y): f(x,y) = 0} at the point a. (c) For the unit vector ū= (-3), find the directional derivative Daf(a). (d) What is the largest possible value for Duf(a) among all unit vectors ü? What is the least possible value? (e) Consider the path elt) = (1,7)+(-), and the composition g(t) = f oct). Find g(0).
(1 point) Find a non-zero vector x perpendicular to the vectors ✓ : 2 and ū -4 -2 =
1. Given the vectors ū=(1,-2,-6) and v = (0,-3,4), a) Find u 6v. b) Find a unit vector in the opposite direction to ū. c) Find (ü.v)v. d) Find 11: e) Find the distance between ū and v. f) Are ū and y parallel, perpendicular, or neither? Explain. g) Verify the Triangle Inequality for ū and ū.
(1 point) In each part, find the two unit vectors in R2 that satisfy the given conditions. 1. The two unit vectors parallel to the line y = -(5x+3) are <1/sqrt(26),-5/sqrt(26)> and <-1/sqrt(26),5/sqrt(26)> 2. The two unit vectors parallel to the line 3x + 6y = 1 are <1/sqrt(5/4),-1/(2(sqrt(5/4))> and <-1/sqrt(5/4),1/(2(sqrt(5/4)))> 3. The two unit vectors perpendicular to the line y = 2x + 3 are <sqrt(575,2sqrt(5)/5> and <-sqrt(5)/5,-2 sqrt(5)/5>
Find all vectors ū that has a magnitude of 7 and forms an angle of 0 = 7 with the positive -axis. HTML Editor T D T = = = = P D x
(1 point) Let Find a basis of the subspace of R4 consisting of all vectors perpendicular to ū.
(1 point) Find a set of vectors {u, v} in R4 that spans the solution set of the equations 0, I w - x - y + 4z | 4w + 2x – y – 2z = =
(1 point) Find the unit tangent, normal and binormal vectors T, N, B, and the curvatures of the curve x = 1, y = -312, z = 31 at t = 1. j+ + + Note that all of the answers are numbers.
2. Let f(x,y) == xy + sin(x). Find a unit vector ū such that for the directional derivative Daf(7,0) one has Daf(1,0) = -_. 27+127. b. None of the other alternatives is correct. Ocū7-7
Given in space the points A(4,7,1), B(2,1,3), and c(0,-1,2) The vectors ū = AB , and ✓ = AC a. (9%) Find ū. v , ū x ū , proj, u b. (3%) Find the area of triangle ABC. c. (3 %) Find the parametric equation of line (AB). d. (3 %) Find the distance from point C to the line (AB). e. (3 %) Find the equation of the plane (ABC). A relatively easy way of getting into international...