12. Let (o) and (1) represent the unit vectors along the x and y directions, respectively....
2. Let A = (cos, sin and B = (cos, sin) be two vectors on the x-y plane. Let C = (cos, sin be another non-zero vector on the x-y plane not collinear with A or B. Show that Ax B = -Bx C. If we could cancel B, as we could if these were real numbers, is it true that A= -Č? 2. Let A = (cos, sin and B = (cos, sin) be two vectors on the x-y...
2. LetA = 〈cos-, sin? and B = 〈cosi' sin, be two vectors on the x-y plane. Let -(cos-, sin π〉 3 4 be another non-zero vector on the x-y plane not collinear with A or B. Show that A × B =-B × C. If we could cancel B, as we could if these were real numbers, is it true that A =-C? [Show your work and conclusions on a separate sheet of paper] 2. LetA = 〈cos-, sin?...
6. Let f(x,y) = xy+sin(x). Find all directions (unit vectors) so that the directional derivative off at the point (1,0) equals -
#1 Exercises with Vectors-II Name [1] Suppose you have two vectors, a and b, that have the same length, so that lal-lb but they point in different directions. Denote the angle between them by . Show that tan(0/2) la-bMa+b Hint: Compute the right-hand side using the fact that lal-bl, and the trig identities 1-cos θ-2sin'(9/2) and 1+cos9-2cos(θ/2) 12] Vectors in 3-dimensions are often parameterized in terms of their length and two angles, as shown in the figure (think of a...
Question 2 Notation: 1, ], and k are unit vectors in the x-, y, and z-directions, respectively. The zero vector is 0; and the scalar zero is 0. What is the result of kk? Selected Answer: Answers: None of the other answers Ofi.e., zero scalar) O fi.e., zero vector) Question 5 O out of 1 points Calculate the vertical reaction force at point C. Report answer to 3 significant digits in N, and assume Cy is positive in the vertically...
(2) Let x-r cos θ, y-r sin θ represent the polar coordinates function f(r, θ) : R. R2, Compute f, (r$) and f, ( ompute * T (2) Let x-r cos θ, y-r sin θ represent the polar coordinates function f(r, θ) : R. R2, Compute f, (r$) and f, ( ompute * T
, A is a linear transformation that maps vectors x in 975 into vectors Let A= 0 -2 1 b in R2 Consider the set of all possible vectors b-Ax, where x is of unit length. What is the longest vector b in this set, and what unit length vector x is used to obtain it? You can use Matlab to save time with the computations, but please justify your answer. , A is a linear transformation that maps vectors...
Q.5: Which statement(s) are correct? a) The unit spatial vectors i and j are exactly the same as the imaginary numbers i orj in complex number theory b) There are certain similarities in that i (orj) is a vector-like quantity and some references even define complex numbers as vectors in two dimensions. c) There are some significant differences in their meaning and the corresponding mathematical operations Q.6: Which statement(s) are correct with respect to an arbitrary vector A illustrated in...
1.) Vectors Can the x or y component of a vector ever have a greater magnitude than the vector itself has? Yes. The x component can, but the y component cannot. Yes, but only when the x and y components have equal magnitudes. Yes. Both components can. Yes. The y component can, but the x component cannot. No. Neither component can. 2.) A force vector has a magnitude of 370 newtons (N) and points at an angle of 53.0° below...
Consider z-f(x,y)-1-xy cos(xy) at (2,-1/2) variations in x and y respectively. and let ΔΧ and ây represent small a) (i) Compute ΔΖ, given that ΔΧ_ 0.028 and Δy_-0.039. 1 1 6DP Az 5DP ii) Write out an expression for dz in terms of x,y and d, dy. dz= 2 (iii) Compute dz assuming dr_Δι and dy_ây dz- 5DP b) Use the equation of the tangent plane to z at (2,-1/2) to approximate Approximate value = 1 5DP Consider z-f(x,y)-1-xy cos(xy)...