Find the Bézier curve (x(t),y(t)) through the points (1,0) and (3,0) with control points (1,2) and (3,2). (1+ 6t² – 4t³, 6t – 6t²) (1+ 2t – 3t2 + t³, 2t – 3t² +t³) O (1+4t² – 2t³, 6t – 6t³ ) (1+ 6t² – 4t³, 3t – 3t2)

Q: Find a plane containing the point (7,3,5) and the line x(t) - 3 + t | y(t) 8 +t z(t) - 3 + 5t

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Q: Determine the intersection of 3x – 4y – 5z = 0 with [x, y, z] = [3, 1, 1] + t [2, -1, 2].

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Q: Determine the point on the plane 2x + 3y − 4z = 0 that is closest to the point P(1, 1, 1)

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Q: (x(t) Find a plane containing the point (2,-4,-2) and the line y(t) z(t) = = = 2 - 5t 4 - 3t 5- 4t

A: Equation of the plane general form is  a(x-x_1)+b(y-y_1)+c(z-z_1)=0

Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = 8x – 6y on the circle…

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Q: Use LaGrange multipliers to find the points on the surface 2² = x² + y² which are closest to (4, 2,…

A: Given surface z2=x2+y2 and the point (4,2,0). The objective is to find the points on the surface…

Q: f(x) = cos(x) and its MacLauren Series representation cos(x) (Α) /1 = 00 Σ ww. Use the Power Series…

A: f(x)=cos(x)      =∑n=1∞(-1)nx2n(2n)! We need to find the Maclauren series of  f(x)=x4cos(x)

Q: Find the line of intersection between the two planes x+2y-z = 5 and x-4y+z=3

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Q: x(t) = 4+ t Find a plane through the point (-1,5,-3) and orthogonal to the line y(t) = 3 - 6t z(t) =…

A: This question can be solved using the concept of lines and planes.

Q: 10. Find an equation of the plane that passes through the points (x, y, z) = (1, 2, −1), (x, y, z) =…

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Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: Find a plane containing the point (-3,-3,5) and the line x(t) y(t) z(t) = = 8 + 4t -4-6t -7-3t

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Q: nd f(3x²+2y)dx- (x+3cos y)dy through the parallelogram with vertices (0;0), (2;0), (3;1) and

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Q: (a) Find two points on the line x = -1+3t, y=t + 2, z= 2t – 7. (b) ( Find The point at which the…

A: Equation are given in parametric form: Vary parametric value for different points.

Q: 2) Find the point of intersection of the plane x - 5y + 3z = -127 and the line r(t) = (-2,-8, 7)t +…

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Q: Find ((x2 + 4y)i + 3 y j) · dř where C consists of the three line segments from (1,0,0) to (1,4, 0)…

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Q: Find the intersection of the plane x - X = y = - 4y - 5z = -137 and the line r(t) = (5, −5, −4)t +…

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Q: v = (2x² – y² +4)i+(5y+3x – 6)j . Consider two closed paths starting (and ending) at a dock located…

A: Let A=(-1,0), B=(2,0), C=(0,2). Now,∫path 1v.dr =∫path 12x2-y2+4dx+5y+3x-6dy…

Q: x(t) Find a plane containing the point (6,-4,4) and the line y(t) z(t) 3 + 3t -3+ t 6 + 3t

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