G. Find the parametric equations of the line tangent to the curve C defined by the vector equation f(t) = (/2 sin t)i – (cos 2t)j+4tk at the point where t = What is the 4 symmetric form of this line?

Q: r(t) = (sin 7t, t, cos t)

A: The vector equation is r(t)=sinπt, t, cosπt. Here, x=sinπt, y=t, z=cosπt Then x=sinπy, and z=cosπy…

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: As per given by the question, there are given: a→t=6t, 5sint, cos6tv→0=4, 3, 5r→0=3, -4, -4 Now, For…

Q: Find the equation of the plane perpendicular to the curve r(t) = (sin(2t), t, cos(2t)) at the point…

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Q: Find parametric equations for the line tangent to the helix

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A: To find the directional derivative of the function at a given point in a unit direction.

Q: Find the set of parametric equations for the tangent line to the graph of the vector-valued function…

A: To find the set of parametric equations for the tangent line to the R(t)=<t+sin3t, t+cos3t,…

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

A:

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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: 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: Find the unit tangent vector T(t) and a set of parametric equations for the tangent line  r(t) =…

A: The given space curve rt=e2ti+cost j - sin3t k. Its derivative is r't=2e2ti-sint j - 3cos3t k. At…

Q: 2. Consider the function 7(t) = (t² - 4,t – 2,v80 + 4t + 7t? - t*). Find parametric equation(s) for…

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

A:

Q: Suppose r(t) = cos(nt) i + sin(t) j+ 3tk represents the position of a particle on a helix, where z…

A: Given the vector

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: Sketch the curve represented by the vector-valued function                               r(t) = 2…

A: Given information: Vector-valued function rt=2costi+tj+2sintk trigonometric identity, sin2t+cos2t=1…

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

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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 the curve     rt=2sin(t),2cos(t),4sin2(t) and the point P1,3,1.

Q: The position of a particle is defined by the vector r(t)=⟨sint,cos2t⟩. Find the maximum speed of the…

A: r(t) = ⟨sint,cos2t⟩ Hence, v(t) = ⟨cost,-2sin2t⟩

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: Find the direction field for the equation: y' = x + sin(y) + cos (x) at the point A = (0, pi3)

A: The direction field also known as slope field is used to graphically represent the solutions of…

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A:

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

A:

Q: Express the given parametric equations of a line using bracket notation and also using i, j. k…

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Q: Find the unit tangent vector and the parametric equation of the line tangent to the given curve at…

A:

Q: Find the parametric equations of the tangent line LT to the curve C:r(t) = 2 cos(t)i + sin(t)j+ 2tk…

A: A parametric equation of a curve is given by: C: r(t) = 2cos(t)i + sin(t)j + 2tk Now, we have to…

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

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: Consider the vector-valued function r(t) = (t2− 2)i + sin-1(t)j +1/(1 + t)k Find parametric…

A: Here, the given vector-valued function is: r(t)=(t2-2) i+sin-1(t) j+11+tk To find the parametric…

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: Find the unit tangent vector to the curve defined by 7(t) = (2 cos (t), 2 sin(t), 4.sin (t)) at t =…

A:

Q: Consider the curve r(t) = (t, 3 cos t, 3 sin t) for t 2 0. Find an equation for the projection of…

A:

Q: Find the unit tangent vector r(t) = t2i + tj + 4/3k and a set o f parametric equations P(1, 1, 4/3)…

A:

Q: Find the parametric equations of the tangent line to the curve represented by the vector function 7…

A: Topic  = Vector

Q: 8. Given the vector r(t) = (sint,cos?, In(cos?)), find the equation of the tangent line in…

A:

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

A:

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A:

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: Consider the following parametric vector function: r(t) = sinti+ cos tj+ sin t k Find the vector…

A:

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)…

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Q: Find the unit tangent vector to the curve defined by 7 (t) = (3 cos (t), 3 sin(t), 5 sin (t)) at t =…

A: we have  r→(t)=3cos(t),3sin(t),5sin2(t) at t=2π3we have to find T→2π3=?and parametric form of…