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2. Consider the line (t) = (4t + 1,3,2-t) and the ellipsoid + + z2 =...
Consider the line x (1,3,2) + t(-1,5,-2) Decide which of the following points lie on the line. (There may be more than one.) a) (1,3,2) (1,5,-2) (0, 8, 0) (2,-2,5) b) Which of the following vectors are perpendicular to the line? (There may be more than one.) (2,0,-1) (10,2,0) (3, 4,2) (0,2,5)
Question 8: [20pt total] Consider the line (1, -3, -1) + t(1,3,2). Q8)a) [12pt] Complete the table below by calculating the relevant points on the line and their central projections onto the plane x = 2 (the first one is done for you). t Point on line Central projection onto r = 2 t=0 (1, -3, -1) +0(1,3,2) = (1, -3, -1) (2, -6, -2) t=1 t = 10 t = 100 Q8)b) (5pt] Determine vanishing point of the line...
- A vector tangent to the parametric curve given by r (t) = <cos (4t); sin (4t); e^(t^2)> at the point (0; 1; e^((pi/8)^2)) is a) (0; 1; e^((pi/8)^2)) b) (0; 4; e^((pi/8)^2)) c) (4; 0; e^((pi/8)^2)) d) (4; 4; e^((pi/8)^2)) e) None of the above - The curve c (t) = (cost, sint ,t) lies on which of the following surfaces: (a) cone (b) cylinder (c) sphere (d) plane (e) none of the above
Consider: S x2-yds, C: r(t) = (e"? 2, 1+e'), te[0,2] Which one of the following "regular" integrals represents the above line integral. dt O a. Ob. V 4 dt 0 S'Vertel dat O d.o Question 8 10 point Consider: | <x?,v/dr, C: r(t) = (sint, cost), te[0,1] Which one of the following "regular" integrals represents the above line integral. S". cost sint - cost sint dt O a. o П 1 sin2tdt 0 s "cost sin’t + cost sint dt...
Please provide clear handwritings for answers and specific step by step explanations of questions 3 and 4. Thank you. 3. Are the plane 6z 3y - 4z-12 and line L 2, y 32t, z2-2t parallel? If so, find the distance between them. If they are not parallel, but are intersecting (at a single point), find the point of intersection. If they are none of the above, draw a cat. 4. The line r(t) = 〈1, 1,1〉 +t(1,3,-1) and the plane...
(1 point) Consider the line L(t) = (2+ 3t, 6-t). Then L intersects: 1. The X-axis at the point (2,6) when t = 0 2. The y-axis at the point (2,6) when t = 0 3. The parabola y = x2 at the points and when t = and
41,43,45 41. Write an equation for a line parallel to f(x)= -5x – 3 and passing through the point (2,-12) 42. Write an equation for a line parallel to g(x)= 3x -1 and passing through the point (4,9) 43. Write an equation for a line perpendicular to h(t)=–2t+4 and passing through the point (-4,-1) 44. Write an equation for a line perpendicular to p(t) = 3t + 4 and passing through the point (3,1) 45. Find the point at which...
Problem 2. Consider the two parametrized curves r(t) = (1+,2-t,t + 382 – 4t + 4) and r(u) = (u?, 3 - u, u' + 22 - 6u + 8), where t and u are in R. (a) Find the coordinates of the point of intersection P of the two curves. (b) The curves traced out by ry and r2 lie on a surface S. Find an equation of the tangent plane to the surface S at the point P...
use Fourier Transforms to convolve f(t) = e-2t u(t-2) and h (t) = e-4t u(t-3). Check your answer by performing the time-domain convolution. use Fourier Transforms to convolve f(t) = e-2t u(t-2) and h (t) = e-4t u(t-3). Check your answer by performing the time-domain convolution.
x = COST TT 7) Find the slope of the line tangent to at t = y = 8 sint 2 1 -" 3 8) Find the length of 0<t<1 1 - 21