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: A Curve a with aca) = (2,4,4), 2e2) = (0 ,2 54). %3D %3D Find Kea), B)

A: We will find out the required value for given curve.

Q: Find a plane containing the point (-5,-8,-7) and the line x (t) y(t) z(t) = = = −7+ 6t -3 - 2t - 2 +…

A: Given;

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: Find the coordinates of the intersection points A and B, between the closed curve (x + 1)² + 4(y-1)²…

A: In this question, we can find the intersection points of the given curve. Using the equation of…

Q: Consider the points + (xo, yo) (x1, y₁) (x2, 12) (X3, 13) (X4, Y4) = = (-3,-4), (-1, 1), (0, 1), X =…

A: x -3 -1 0 2 3 y -4 1 1 5 9

Q: Consider the following lines: r(t) = (3t + 2, 2t +2, 4t + 4), R(t) = (s+ 1, 4s – 2,-5s + 9), -o 0…

A: The given lines are                      r(t)=3t+2, 2t+2, 4t+4   , -∞<t<∞ and…

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: 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: 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: A triangular plate occupies the triangular region D with vertices (1,0), (5,0), and (1,4). The…

A: Given vertices of a triangular region are (1,0), (5,0), and (1,4) and the temperature at each point…

Q: 2. Use Lagrange multipliers to find the point on the curve g(x, y) = 2x + y2 = 0 that is closest to…

A: Given:The equation of a curve is .To Find:We have to determine the point on the curve  that is…

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: Determine which of the following points are in the plane 3(x − 2) + 2(y + 3) − 4(z − 4) = 0: (a) (0,…

A: To check whether the given points are in the plane or not, substitute given values in the equation…

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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Q: 4. Uine segment XY has endpoints X (5, 7) and Y (-3, 3). Find the equation for the perpendicular…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let A(0,-2), B(0,4) (1) Find the set of all points P(x, y) such that m(PA)=2 m(PB) (2) Convert the…

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Q: If UW = 4t- 16 and UY = t + 14, find UY in rhombus VWXY.

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