project3 - x = x y = y z = z x = 3/(2*l) y =-1/(4*l) z =...

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1) A) syms x y z l e = (x.^2+2*y.^2+3*z.^2-1); dee = [diff(e,x), diff(e,y), diff(e,z)] dee = [ 2*x, 4*y, 6*z] p = 3*x - y + 3*z – 1; dpp = [diff(p,x), diff(p,y), diff(p,z)] dpp = [ 3, -1, 3] dp = l*dpp dp = [ 3*l, -l, 3*l] point = dee - dpp point = [ 2*x - 3, 4*y + 1, 6*z - 3] f = solve('2*x*l = 3', '4*y*l =- 1', '6*z*l=3','x^2+2*y^2+3*z^2-1') f = l: [2x1 sym] x: [2x1 sym] y: [2x1 sym] z: [2x1 sym] [f.x,f.y,f.z,f.l] ans = [ (3*2^(1/2))/5, -2^(1/2)/10, 2^(1/2)/5, (5*2^(1/2))/4] [ -(3*2^(1/2))/5, 2^(1/2)/10, -2^(1/2)/5, -(5*2^(1/2))/4]
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Unformatted text preview: x = x y = y z = z x = 3/(2*l) y =-1/(4*l) z = 1/(2*l) dval = dee[x, y, z] b) syms X Y Z h = [(X-x), (Y-y), (Z-z)] h = [ X - 3/(2*l), Y + 1/(4*l), Z - 1/(2*l)] syms r s x y dot( f=(1-3*x+y)/3; ezsurf(sin(r)*cos(s),(sin(r)*sin(s))/sqrt(2),(cos(r))/sqrt(3)) hold on ezmesh(f,[-1,1,-1,1]) 4) clear all; syms x y z ezsurf(x,(-x.^2-z.^2)/4,z) b) s1 = x.^2+4*y+z.^2 s1 = x^2 + z^2 + 4*y %solving for the tagent of S1 vect = [diff(s1,x), diff(s1,y),diff(s1,z)] vect = [ 2*x, 4, 2*z] vect(0, -1, 2)...
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project3 - x = x y = y z = z x = 3/(2*l) y =-1/(4*l) z =...

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