5. Find the parametric equations of the line tangent to the curve C defined by the vector equation () = (V2 sin t)t – (cos 2t)/ + 4ck at the point where t ==. What is the symmetric form of this line?

Q: (9.) r(t) = (1, cos t, 2 sin t)

A: As per your query the solution of question no 9 is given the next step.

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: Give a vector parametric equation for the line through the point (3, 1) that is perpendicular to the…

A:

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: The given curve is rt=t2+1,4t12,et2-t. Notice that the given curve satisfies t=1(If t=1 is plugged…

Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…

A:

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

A:

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

A:

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 curve of intersection of the surfaces…

A: Given surfaces are And the given point P is

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

A:

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: Given:

Q: A curve is defined by the parametric equations: x(1) = e' cos t, y(t) = e' sint d²y dy and dr of the…

A: It is given that, x(t)=et cost,y(t)=et sint   It is known that, dydx can be found by chain rule and…

Q: 4. Determine the directional derivatives of $(x, y) = tan"2+3 sin ). at the point (1,1) in the…

A:

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

A:

Q: Find a vector equation for the tangent line to the curve 7(t) = (5 cos(6t)) i + (5 sin(6t)) j+…

A: Given the vector function, r(t), we call r′(t) the tangent vector provided it exists and provided…

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

A:

Q: Find an equation of the tangent(s) to the curve with parametric equations tsint at the point…

A:

Q: Eliminate the parameter t from the parametric equationsx =3 +sin t and y = cos t - 2.

A: Given: x=3+sint and y=cost-2 We have to eliminate the parameter t from the parametric equations.…

Q: 4. Find the parametric equation of the tangent line to r(t) = 4costi – 3tj %3D at Po(2, –n)

A: Given: To find the parametric equation of the given tangent line as follows, r(t) = 4 costi- 3tj…

Q: s) Find the parametric equations of the line that is perpendicular to the plane 2x +y+3z = 4 through…

A:

Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 2x + 4y +…

A: Equation of line normal to graph of functions f(x) is :  r&lt;t&gt; = &lt;x0,y0,z0&gt; +…

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A:

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

A:

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

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: Find the length of the curve whose parametric equations are x = 3t^2 and 3t^3, from t = 0 andt = y =…

A:

Q: п 4. Find the slope of the tangent line to the polar curve r = 1 – sin40 at 0 = 4 : a. 3 b. 4 c. 2…

A:

Q: Find an equation of the tangent(s) to the curve with parametric equations x = 1+ vt, y = e at the…

A:

Q: Find the 1st and 2nd derivatives of y with respect to x from parametric equations. a). x=3 (t + 2)…

A: First differentiate x and y wrt t then divide

Q: Find parametric equations for the line tangent to the helix r(t) =(sqrt(2)cos t)i + (sqrt(2) sin t)j…

A:

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

A: Topic  = Vector

Q: Which one of the following equations is the equation of the tangent plane to the surface xy + xz +…

A:

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

A:

Q: Find a vector equation for the tangent line to the curve 7(t) = (5 cos(6t)) i + (5 sin(6t)) j +…

A:

Q: 11. C is the curve F(t) = ( In (2 Vt +3 Find parametric equations for the tangent line to C at the…

A: Note: Here, the given point (0,1,2) is incorrect there should be(0,-1,2) because the point is on the…

Q: 2. Find a set of parametric equations for a particle that oscillates on the line y = 6x – 5 between…

A:

Q: 7. Sketch the curve with parametric equations x = e-t , y = e', teR.

A: Topic = Functions

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: Answer

Q: 11. C is the curve F(t) = (In (2 – t), V+3). Find parametric equations for the tangent line to C at…

A: According to question,Given Curve C,Ft = ln2-t, 1t-2, t+3

Q: 2. Find parametric equations for the tangent line to the curve r(t) = (t8,t³,t7) at (1,1,1).

A:

Q: 9.) a. Find the parametric equations for the tangent line to the Curve at' the Specific point. X =t°…

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: 2. Find the parametric equations for the line tangent to the curve given by r(t) = cos ti + sin tj +…

A:

Q: 4. If a particle moves in the xy-plane so that at time t its position vector is sin 31 ,3r2 find the…

A:

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

A:

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

A:

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A:

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.