Find a parametric equation of the line tangent to 7 (t) at the point (– 12, 144, – 4.159)

Q: Consider the smooth parametric curve 6 defined by the equations t (t²-3) { 3 (t²- 3)' = = where t€…

A:

Q: Find a set of parametric equations for the tangent line to the graph at t = to. (Enter your answers…

A:

Q: Let 7(t) = Find a parametric equation of the line tangent to 7 (t) at the point (– 31, 189, 10.832)…

A: Letr→(t)=-t3-4,t3+2t4,-4ln(5t)We need to determine a parametric equation of the line tangent to…

Q: Consider the curve C given in parametric equations as t(t – 1)2 In (4t² + 1) %3D C : for t e R. (a)…

A: Given problem is :

Q: Find the equation of the tangent line(s) to the following set of parametric equations at the given…

A: The equation of a line can be obtained by using the expression y-y1=m(x-x1). Here, m is the slope of…

Q: Sketch the parametric curve of the given parametric equations and indicate the orientation. 1. x=3t…

A:

Q: Let 7(t): Find a parametric equation of the line tangent to 7(t) at the point (1, – 3, – 3.466)…

A: let r→(t)=<5t3-4,t4-4t4,-5ln(2t)>r→(t)=<15t2,4t3-16t3,-5t>And r0=<1,-3,-3.466>Now…

Q: Let 7(t) = Find a parametric equation of the line tangent to 7 (t) at the point ( – 5, 3, – 2.773)…

A: The given vector is r→(t)=-2t3-3,t4+2t4,-4ln(2t)  , we have to find a parametric equation of the…

Q: Find the equation of the tangent line (s) to the following set of parametric equations at the given…

A: Given parametric equations of a curve.

Q: 8. Given the space curve r(t) = (sin²t, cos't, tant), find an equation of the tangent line in…

A:

Q: Find the parametric equation of the line through a = 3 A co which is parallel to b = 2

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Q: Q6) The parametric equation of the x_axis is: * O t-1 O x=0 O x=t O x=1

A: Since at x-axis, y and z axis are both zero and only x is varying so general parametric equation for…

Q: Sketch the plane curve r(t) = a cos3 ti + a sin3 tj and find its length over the given interval [0,…

A: The curve is r(t)=a cos3ti + a sin3tj   Interval is 0, 2π

Q: Determine the exact length of the curve for the parametric equation x = tsint and y = tcost for 0 ≤…

A: To find the exact length (arc length) of the curve for the parametric equation x=t sin(t), y=t…

Q: The parametric equations that correspond to T= (2t 1) i- 3vtj+ sin 3t k is %3D

A:

Q: 19. Find y' in the parametric equations x =, t-1 t+1 A) (f – 1) 7-1 B) (1+ 1)? 2 +1 C) (1+1)? t +1…

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Q: Consider the curve C in R³ defined by the parametric equation c(t) V2 v2 T = (cos(t), sin(t), t).…

A:

Q: Consider the parametric curves r(t) = - cos(t) y(t) = ; sin(t) in 7 <t < 2m (a) Eliminate the…

A: We need to use Trigonometry identities

Q: Find the equation of the line tangent to the graph defined by the parametric equations 3 x =t2 – 6…

A: First evaluate the point of contact by substituting 4 for t in the given functions x and y. x=432-6…

Q: Consider the smooth parametric curve defined by the equations = t (t²-3) { = 3 (t²-3) ¹ where t € R.…

A:

Q: Let 7 (t) = Find a parametric equation of the line tangent to 7(t) at the point (5, 20, 1.792) x(t)…

A: First, we need to find the derivative of the given parametric curve as shown below:…

Q: find the decomposition of a(t) into tangential and normal components at the point indicated r(0) =…

A: v⇀(θ)=r'⇀θ=-sinθ,cosθ,1a⇀(θ)=v'⇀θ=-cosθ,-sinθ,0…

Q: -2 Find the projection of v = 1 onto the line l of R³ given by the parametric equation l = tủ, where…

A: We will find out the required projection.

Q: Let 7' (t) = Find a parametric equation of the line tangent to r(t) at the point (59, 0, - 2.303)…

A: Follow the procedure given below.

Q: Let 7(t) = Find a parametric equation of the line tangent to 7(t) at the point (7, 5, 1.386) x(t) =…

A:

Q: . Find a cartesian equation for the given parametric equations: a) x = t2 – 4 and y =t+1 b) x = 2…

A: Eliminating t

Q: Find the points on the parametric curve c(t) = (3t 2 − 2t,t 3 − 6t)where the tangent line has slope…

A: This question is taken from the tangent and normal in which we have to find points on the given…

Q: 10b. Find the parametric equations of the tangent line to the curve at t =1.

A: Given: The position vector is of a particle in space at a time t : r→(t)=&lt;t+1,t,1t&gt;=&lt;x, y,…

Q: Which is a parametric equation for the curve 25 = (x +7) + (y+ A. c(t) = (5 cos(t) – 5, 5 sin(t) –…

A:

Q: A curve C is defined by the parametric equations x(t) = 3 + t“ and y(t) = t° + 5t.Which of the…

A: Given,         A curve C is defined by the parametric equations xt=3+t2 and yt=t3+5t.

Q: (c) (d) Determine the exact length of the curve of the conic section from 0 = 0 to 0 = π/6. Explain…

A:

Q: A curve C is defined by the parametric equations x(t) y(t) = 8t³ – 2t² + 4. Write the equation of…

A:

Q: Consider the following parametric curve: x(t) = 3t^2 −6 and y(t) = 3t^4 −3t^2 +12t +10 Find the…

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Q: express the parametric curve in the form y = f (x) c(t) = (4t − 3, 10 − t)

A:

Q: ) Suppose that the parametric equations x = 1, y = r', 12 0, model the position of a moving object…

A: Given

Q: Which is the graph of the derivative dyldx of the parametric equations x(t)= 3cos t and y(t)=3sin t…

A:

Q: To calculate the derivative dy/dx of the parametric equations x(t)= 3cost and y(t)=3sin t for…

A:

Q: 1. Consider the graph of r(t) = 2t i+ tj +t° k Determine parametric equations of the tangent line to…

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Q: Find the equation for the line tangent to the parametric curve: at the points where t = 5 and t =…

A: Solution is given below:

Q: The parametric equation of the x_axis is t=1 O x=1 O x=0 O x=t

A: To find the parametric equation of x axis.

Q: 12. Sketch the plane curve defined by the given parametric equations, and find an x-y equation for…

A: The given parametric equations are,

Q: 1 '1+t²⁹ Given R'(t) = (4e²t, , 2cosh t), and R(0) = (1, -2,3).

A:

Q: Let 7 (t) = Find a parametric equation of the line tangent to 7(t) at the point (– 27, – 44, 1.792)…

A:

Q: Let 7(t) = %3D Find a parametric equation of the line tangent to 7(t) at the point (– 321, 234,…

A:

Q: Find the parametric equations of the line L which is parallel to the line L1 : 2x = 5y = 7z and…

A: The parametric equation of a line L that passes through a point a and parallel to a line r is given…

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: Sketch the curve r= cos 2θ

A: Symmetric test for polar coordinates r=f(θ): If f(θ)=f(-θ) then graph is symmetric about polar…

Q: Let 7(t) = - Find a parametric equation of the line tangent to T(t) at the point (731, 1296, –…

A:

Q: Consider the smooth parametric curve defined by the equations t (t²-3) { = = 3 (t² - 3)' = where t E…

A:

Q: Let 7(t) = Find a parametric equation of the line tangent to 7(t) at the point (– 13, 96, – 2.079)…

A:

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.