Let C be the parametric curve (1) Determine the point(s) of intersection of C with the xz plane. (2) Determine the...
Let the curve C in the (x, y)-plane be given by the parametric equations x = e + 2, y = e2-1, tER. (a) Show that the point (3,0) belongs to the curve C. To which value of the parameter t does the point (3,0) correspond? (b) Find an expression for dy (dy/dt) without eliminating the parameter t, i.e., using de = (da/dt) (c) Using your result from part (b), find the value of at the point (3,0). (d) From...
(1 point) A parametric curve r(t) crosses itself if there exist t s such that r(t)-r(s). The angle of intersection is the (acute) angle between the tangent vectors r() and r'(s). The parametric curver (2 -2t 3,3 cos(at), t3 - 121) crosses itself at one and only one point. The point is (r, y, z)-5 3 16 Let 0 be the acute angle between the two tangent lines to the curve at the crossing point. Then cos(0.997 (1 point) A...
Please solve it quickly Thanks ❤ a. Let C be the curve which is represented by the vector valued function r(t) = xi + /2; +*+?k, Osts 2. Find the arc length of C. b. Let C be the curve with parametric equation x = 2t? and y = 8+9+ t, then find the equation of the tangent line to the curve C corresponding to the point t = 1.
uestion 7[value16jp (a) Find parametric equations for the tangent line to the curve of intersection of the cvlinders y -r2 and z - r2 at the point (1, -1,1) (b) Find an equation for the osculating plane of the curve ア(t) 〈cos 3t, 4t, sin 3t) at the point (-1.4T,0). uestion 7[value16jp (a) Find parametric equations for the tangent line to the curve of intersection of the cvlinders y -r2 and z - r2 at the point (1, -1,1) (b)...
QUESTION 2 Let C be the curve represented by the parametric equation x(t) = ? +61 +12t+36 yt=+1 Find an equation for the tangent line at the point t-1 on the curve C. Where on the curve is the tangent line vertical? Attach File Browse My Computer QUESTION 3 Express the Cartesian coordinates (-1,1) in polar coordinates in at least two different ways. Attach File Browse My Computer
(1 point) Find the point of intersection of the two linesh : x = 〈10, 18, 3〉 + t 〈4-k-2) and 12 : X = 〈 18, 19, 20) + t 〈 Intersection point: 4, 0-5) (1 point) The plane π is defined by the vector-parametric equation π : x(s, 1-(1,-8,6) + s 〈-1,-4,-3〉 + 1 〈3,-4,0). Find an equation for π in general form Plane equation (1 point) Find the point of intersection of the two linesh : x...
1. a. Consider the curve defined by the following parametric equations: r(t) = et-e-t, y(t) = et + e-t where t can be any number. Determine where the particle describing the curve is when tIn(3) In(2). 0, ln(2) and In(3). Split up the work among your group Onex, vou l'ave found i lose live polnia, try to n"惱; wbai ille wlu le curve "u"ht lex k like. b. Verify that every point on the curve from the previous problem solves...
Find a normal vector and an equation for the tangent plane to the surface: x3 - y2 - z2 - 2xyz + 6 =0 at the point P : (−2, 1, 3). Determine the equation of the line formed by the intersection of this plane with the plane x = 0. [10 marks] (b) Find the directional derivative of the function F(x, y, z) = 2x /zy2 , at the point P : (1, −1, −2) in the direction of...
2. Let A:(-1,1,-1), B:(2,0.2), C:(4.1.-3), and D:(-3, 1, 10) be points in R. (a) Find the angles (in degrees) of the triangle with vertices A, B and C. (b) Find an equation of the plane passing through the points A, B, and C. (c) Find two unit vectors perpendicular the plane through A, B, and C. (d) Find the volume of the tetrahedron with vertices A, B, C, D. 3. (a) Find an equation of the tangent line to the...
1. (1 point) Find the arc-length parametrization of the curve that is the intersection of the elliptic cylr 1 and the plane z-2y = 7. Use s as the arc length parameter with s = 0 corresponding to the point (0, 1.9) oriented counter-clockwise as seen from above Spring 2016) 1. (1 point) Find the arc-length parametrization of the curve that is the intersection of the elliptic cylr 1 and the plane z-2y = 7. Use s as the arc...