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    <p>The following code gets you a long way, I think. See example output: <img src="https://i.stack.imgur.com/QH0cL.png" alt="enter image description here"></p> <p>I added enought comments that you should be able to take it from here...</p> <pre><code>% plot ellipsoid in 3D % height and width of ellipsoid: e_h = 10; e_w = 3; % position where the "quivers" (arrows) go: q_offset = 2; % distance from axis q_scale = 0.5; % multiplier to give parabola some size q_spacing = 0.5; % distance between arrows q_height = 2.5; % height above XY plane where arrows are drawn N = 1000; % number of points for drawing theta = linspace(0, 2*pi, N); % parameter to help drawing ellipse zerov = zeros(1, N); % array of zeros that I will need % coordinates of main ellipse: x = e_w * sin(theta); y = zeros(size(x)); z = e_h * cos(theta); % plot main ellipse: figure; plot3(x, y, z) % secondary plot y2 = q_scale*(e_w.^2 - x.^2) + 2; % offset parabola - what your plot looked like... hold on plot3(x, y2, zerov+q_height); % plotting the parabola in the XY plane at height axis equal % make the plot dimensions isotropic % add quivers q_base = -e_w:q_spacing:e_w; % x coordinate; y and z are fixed q_length = (e_w.^2 - q_base.^2)*q_scale; % length of quiver - just an equation I chose q0 = zeros(size(q_base)); % another vector I will need multiple times q1 = ones(size(q_base)); % ditto % plot the arrows: the "-1" argument means "don't scale" quiver3(q_base, q0+q_offset, q_height*q1, q0, q_length, q0, -1) </code></pre>
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