Find equations of the normal plane and osculating plane of the curve at the given point. x = sin 2t, y = cos 2t, = 4t, (0, 1, 27) = Z

Q: Find the distance between the origin and the normal to the curve y=e2x+x2 at the point where x=0…

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Q: X 1 (A) If g tan , find the derivative 1² +2 yz of g at point (1,2,-1) in the direction of the…

A: Directional derivative of the function

Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

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Q: Q1/Find the tangent and normal vector for curve = (5sin n i+5 cos n j+n k)

A: we have to find the tangent and normal vactor

Q: Q1) Find the tangent &normal vector for the curve r-asint?i+acos tj +bt?k

A: Given that The position vector is r→=a sin t2i→+a cos t2j→+bt2k→   The tangentT→ vector is given by…

Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

A: We have to find

Q: Find the principal unit normal vector to the curve at the specified value of the parameter.

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Q: 4.a. Find the unit tangent and normal vectors to r(t) = 4 cost i + sin t j at t = /2. Sketch a…

A: Given that rt=4cost i +sin t j Then r't=-4sin t i  +cos t. The formula for tangent vector is…

Q: Find the principle unit normal vector to the curve given below at the specified point. r(t) = ti+…

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Q: Find equations of the following. 2(x - 9)2 + (y - 2)2 + (z - 8)2 = 10, (10, 4, 10) %3D (a) the…

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Q: Find the principal unit normal vector r(t) = cos 3ti + 2 sin 3tj + k to the curve at the specified…

A: To find the principal unit normal vector of r(t)=cos 3t i + 2 sin 3t j+k with t=π first…

Q: Find an equation for the tangent plane and parametric equations for the normal line to the surface…

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Q: Find an equation of the tangent plane and find a set of symmetric equations for the normal line to…

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Q: 5. Given that r(t) = 3i + e* sin tj + e cos tk Find equations of the normal plane and osculation…

A: We have to  find equation of normal and oscillating plane of above curve.

Q: Find an equation for the tangent plane to x? + y – 8xy + 4x – 5y – 9z = 765 at the point (-9, 9,…

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Q: Find the length of the curve with parametric equations x = e' · cos t, y = e' sin t, with 0 <t <…

A: Given x = et.cos(t) y = et.sin(t)

Q: 6.) Find the principal unit normal vector to the given curve at the specified value of the…

A: Given: r→t=3cos2ti+3sin2tj+tk, t=π12

Q: 6. Find the unit normal vector to the curve r(t) = (2sint,5t,2 cos t)

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Q: III. Find the parametric equations of normal line to the surface given by f(x, y) = tan 2 V + y? at…

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Q: Q3/ find equations for the (a) tangent plane and (b) normal line at the point Po on the given…

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Q: (iii) Given the curve with parametric equation x = e and y = In(2-r²) Find the equation of the…

A: Formula: The normal line of the parametric equation x=ft and y=gt at the point t=t0 is the line…

Q: find the curve’s unit tangent vector. Also, find thelength of the indicated portion of the curve. .…

A: Given:                  rt=cos3tj+sin3tk,     0≤t≤π2                 v=ddtrt=ddtcos3t j+sin3t…

Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

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Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

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Q: Consider the following. x = sin(2t), y = -cos(2t), z = 8t; (0, 1, 47) Find the equation of the…

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Q: Q6|| Find the tangent plane and normal line of the surface x+y+z=1 at the point p(0,1,0).

A: Equation of tangent plane is Fx(x-x0) +Fy(y-y0) + Fz(z-z0) =0  F = f(x, y) =k

Q: Find and equation of a) the tangent plane and b) the normal line to the given surface at the…

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Q: Find equations of the following. y = x2 – z?, (10, 19, 9) (a) the tangent plane 2 y z= (b) the…

A: Here in the given question, the tangent plane f(x, y) is given as: z=fx,yy=x2−z2z=x2−y  at…

Q: Find an equation of the plane tangent to the following surface at the given point. z= tan (xy):…

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Q: find an equation of the normal plane through the point t=pi/3.  r(t) = 2sin(t)i+. 4cos(t)j +tk

A: Given curve is r(t)=2sin(t)i+4cos(t)j+tkr'(t)=2cos(t)i-4sin(t)j+k At t=pi/3…

Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

A: Given that : r(t) = cos(3t) i + 2sin(3t) j + k and t= π. Find the principal normal unit vector to…

Q: Find equations of the following. 2(x – 7)2 + (y – 5)² + (z – 6)² = 10, (8, 7, 8) %3D - (a) the…

A: Suppose we have given a surface .Then; The equation of tangent plane at   is  . The equation…

Q: Find the Tangent vector, the Normal vector, and the Binormal vector (T, N and B) for the curve r(t)…

A: This question can be solved using the concept of vectors and derivatives.

Q: Prove that the segment of the normal to the curve x = 2a sint +a sint cos't, y = -a cos't contained…

A: First find derivative then equation of normal line ,and point of coordinate axes and then use…

Q: For the curve defined by 7(t) = (e-, 3t, e') find the unit tangent vector, unit normal vector,…

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Q: Consider the curve in space 7 (t) = (t², t³, t+) (1) Find an equation of the tangent line at t = 1…

A: Topic:- equation of tangent and normal plane to the curve

Q: Find a standard equation for the tangent plane and parametric equations of the normal line at the…

A: Introduction: If F(x,y,z) is a differentiable surface at the point (x0,y0,z0), the tangent plane to…

Q: Q5: Find equations for (a) the tangent plane and (b) normal line at the point P, on the given…

A: Given that  The equation  cos(πx)-x^2y+e^(xx)+yz=4  Point (0,1,2) To find the equation of the…

Q: 4. Let g(x, y) = e"/v, Find an equation for the tangent plane at (x, y) = (2, 1).

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Q: Find an equation for the tangent plane and parametric equations for the normal line to the surface…

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Q: Find an equation of the plane tangent to the following surface at the given point. z = tan (xy);…

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Q: Q5: Find equations for (a) the tangent plane and (b) normal line at the point P, on the given…

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Q: Consider the following. x = sin(3t), y = -cos(3t), z = 6t; (0, 1, 2n) Find the equation of the…

A: Given :- The given curve x = sin 3t ,  y =-cos 3t  , z =6t   ;  0,1,2π To determine :- The equation…

Q: Find the principal unit normal vector to the given curve at the specified value of the parameter.…

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Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

A: Consider, r(t)=lnt4i+t-4t+8j+t lnt4kWe first evaluate r(t) at t=t0=4r(4)=ln44i+4-44+8j+4 ln44k…

Q: Consider the curve in space 7 (t) = (te", vt, v2t) (1) Find an equation of the tangent line at t = 1…

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Q: Find the normal line, of the parametric. curve = t. the point t=2 et 1++

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Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

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