Q.1 Find the parametric equation of the line that 1) Let L1: x = 2t – 1, y = 3 +t,z = t – 1/2 Find a) Vector parallel to L1 b) Points lies on line L1 c) When the line L1 intersects zy- plane.

Q: 2 7 Find the projection of v = -1 onto the line tlof R'Igiven by the parametric equation e = tul…

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Q: x = t + t and y = t* + 2t²

A: If the parametric equation of a curve are x=f(t) and y=g(t), then the slope of the tangent line at…

Q: Find the real number a such that the line of x = 1, y = 2-1, z=3+t, the plane of equation parametric…

A: Given parametric equations are x=t , y=2-t, z=3+t Where t∈ℝ and  Plane is αx+5y+z-10=0

Q: 33 and Complete the parametric equations for the line where the planes – 3x – 9y – 12z = - 11x + 2y…

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Q: Let C be the curve of intersection of the hyperboloid x2−y2+z2 = 4 and the plane 2y−z = 0. Find…

A: Let C be the curve of intersection of the hyperboloid x2 - y2 + z2 = 4 and the plane , 2y - z = 0.…

Q: Find parametric equations representing the line segment joining P(-4, 1) to Q(3, –2) as (æ(t),…

A: We have to find parametric equations to represent the line segment from P(-4,1) to Q(3,-2).

Q: Which of the following is the parametric equation of the line through the point (1,2,3) and parallel…

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Q: Find a parametric form for the line through the point (8, –6, –3) and perpendicular to the plane 2x…

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Q: 6. Find the projection of v = | -7 onto the -2 line l of R given by the parametric equation l = tủ,…

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Q: a) By first sketching its projection onto the yz-plane, sketch the curve r(t) = (t, cos(t), 2…

A: For (a), We will plot the sketch of r(t)=t, cos(t), 2 sin(t),  0≤t≤4π onto the yz-plane (that means…

Q: (а) Given two points P(6, 3,1) and Q(5,0,0), find the parametric equations for a smooth curve, C:x =…

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Q: 17. Find the cartesian equation of the parametric curvex =1+e²*, y= e'. (a) z² = y? – 1 (b) 7 = x² –…

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Q: A Cartesian equation for the parametric curve x=24sin?e, y=21cos20, n ses 31/2 is given by O…

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Q: 5. Find the parametric equations of the line tangent to the curve C defined by the vector equation…

A: To find the parametric equation of the given tangent to the curve. The vector equation of the curve…

Q: Q3/ Find the real number such that the line of parametric equations x = t, y = 2 - t, z= 3+t, is ax…

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Q: Find the unit tangent vector T(t) and find a set of parametric equations for the line tangent to the…

A: Given that rt=3cost,3sint,9 P32,32.9 To find the parametric equation for the line tangent to the…

Q: 16. Sketch the parametric curve x = Vt, y= sin t, 0<t< 2n. (b) (a) 1.0 (c) 101 1.0 0.5 0.5 0.5 05 10…

A: The graph of the parametric curve x=√t, y=sint , 0≤t≤2π is given as below,

Q: Find the real number a such that the line of parametric equations x = t, y = 2 – t, z = 3 + t, te R…

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Q: A particle moves in space along a path whose parametric equations are given by bsin(wt), x2 =…

A: Image is attached with detailed solution.

Q: Consider the graph of r(t) = 2t^2i + t^2j + t^3 k Determine parametric equations of the tangent line…

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Q: TRUE OR FALSE. A plane curve C defined by the parametric equations x = f(t) and y = g(t), where t is…

A: check the given statement is true or not.

Q: Consider the planes 71 : x - 2y + 3z +1 = 0 and 72 : 2x + y+z+2 = 0. Let l be the line of…

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Q: Let l be the line y = - (7x + 5) in R21 Find vectors dland b so that v = a + tblis a parametric…

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Q: 1. Find the parameter λ in the parametric form of the line l z+2 6:2-3-9-1-2-20 l: = X y so that…

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Q: Consider the surface S of equation 2 = x² + y*" An equation for the tangent line tangent to S at…

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Q: What is the parametric equation of line through the point (1,2,-1) and perpendicular to the plane…

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Q: 2. Consider the curve traced out by the vector valued function r(t) = (sin t cos t, cos? t, sin t)…

A: given that r(t)=(sintcost,cos2t,sint) we need to show that the curve lines on the surface of the…

Q: Which of the following is the parametric equation of the line through the point (1,2,3) and parallel…

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Q: Suppose F(x, y) = (5x – y)ỉ + xj. %3D (a) Find a vector parametric equation for the line segment…

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Q: 6. Find a set of parametric equations for the line tangent to the space curve at the given point. 2…

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Q: r(4)=DTsin(i+ 34 j+ t°K 2. POINT: (1,2,1)

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Q: Which of the following is Parametric equations for the line passing through the origin and A(1, 0,…

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Q: Find an equation of the line through (0,0,0) that is parallel to the e parametric equations x(t) = 2…

A: To find out equation of any line we need one point on the line and a vector which is parallel to the…

Q: Consider the line perpendicular to the surface z=x^2+y^2 at the point where x=3 and y=2. Find a…

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Q: Match the parametric equation with the corresponding plane curve displayed. Sx=47-5 y=16 130 104 78…

A: The given parametric equation is: x=4t2-5y=16t4

Q: Use definition 13.7.1 to find the equation of the tangent plane and the parametric equations for the…

A: Let the given function is,

Q: Let C be the curve of intersection of the spheres x 2 + y 2 + z2 = 3 and(x - 2)2 + (y - 2)2 + z2 =…

A: Let fx=x2+y2+z2-3=0 &amp; gx=x-22+y-22+z2-3=0 At P=(1, 1, 1) ∇f=2x, 2y, 2z∇fP1, 1, 1=2, 2, 2…

Q: Consider the smooth parametric curve C₁ defined by equations t³-t²- 2t Xx y = = (161²- 48t +35) NIW…

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Q: Which of the following is the parametric equation of the line through the point (1,2,3) and parallel…

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Q: Allow A be the point with Cartesian coordinates (6, 9), and D be the plane curve with parametric…

A: The slope of the tangent to the curve: y=fx at x=a is f'a. The point-slope form of a line that…

Q: A curve is defined by the parametric equations z (t) = at and y (t) = bt, where a and b are…

A: Given,  We have  xt = at   and yt = bt  ;  where a and b are constants.  We have to find the length…

Q: What is the parametric equation of line through the point (1,2,-1) and perpendicular to the plane…

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Q: 38. Let r(t) = (1³ -1- 2)i + 4r* j. %3D (b) Find parametric equations for the tangent line to the…

A: Topic = Vector

Q: Find a set of parametric equations for the line passing through the point       (1, 0, 2) that is…

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Q: A curve in the plane is defined parametrically by the equations x = t +t and y t* + 2t2. An equation…

A: The equation of the tangent line is: y-y1=mx-x1 Where m is the slope of the tangent line. And The…

Q: The planes 5x+ 2y + 2z = 5 and 3x + 5y = -22 are not parallel, so they must intersect along a line…

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Q: 1. Let C be the parametric curve defined by Determine if C is concave up or concave down at…

A: Given parametric curve isx(t)=t2-t-2,y(t)=t3-12t2+tThe concavity of the curve C at the point -2, 32…

Q: G. Find the parametric equations of the line tangent to the curve C defined by the vector equation…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.