Q2. A particle is moving along the curve whose position vector is given as R(t) = (t) i+( In (cost)) j at the interval - (1/2) < t < (x / 2), find the : a) Speed at any time. b) Unit normal vector. c) Path curvature.

Q: vector-valued function 7(t) the parametric equations of the line.) b) Find the distance of the point…

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Q: 1. Let ř(1) = . Find a vector and parametric equation of the line tangent to F(1) at the point (-…

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Q: 3. Consider the following helix with vector equation 7 (t) = 2 cos (t) 7 (t) 7 + tỉ + 2 sin (a)…

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Q: The length of a curve given parametrically by x = x(t), y = y(t), and z = z(t) for a ≤ t ≤ b in the…

A: Given information: Parametric equation of curve is : x=x(t)y=y(t)z=z(t) We need to find the length…

Q: 6. Find a vector which is normal to the currive: 3= 11 at (1,2). x³ + xy + y²

A: We have to find a vector which is normal to the curve: x³ + xy + y³ = 11 at (1,2).

Q: 2. For this entire page, let r(t) = (4 sin(t), 3t, 4 cos(t)) (a) Circle the correct graph for the…

A: The objective of this question is to understand the properties of the vector function r(t) = (4…

Q: For the curve defined by 7(t) = (e-t, v2 - t, e*) find the unit tangent vector and unit normal…

A: A detailed solution is given below.

Q: Find the unit tangent and unit normal vectors T(t) and Ñ(t) given 7(t) = (3/2t, e3t, e¬3t). Also,…

A: Given that r→t=32t,e3t,e-3t. Find the value of r→'t and r'→'t.…

Q: 5. Consider the curve whose equation is (x² + y²)² = 9 (x² - y²). Find a normal vector and a tangent…

A: First we find partial derivatives of f(x,y) w.r.t x and y. Then find general tangent vector normal…

Q: 6. Find an equation of the tangent plane and a set of symmetric equations of the normal line to the…

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Q: A car travels over the hill having the shape of a parabola. When the car is at point A, it is…

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Q: The vector function r(t)=sin 2ti−cos 2tj+t√√5k determines a curve C'in space. i. Find the unit…

A: Given: rt=sin2ti-cos2tj+t5k To find: i. The unit tangent vector T and the principal unit normal N.…

Q: 1. Consider the position vector r(t) = (t³) i + (3t) j + 4k and at t = 1 find the: (a) curvature,…

A: The general form of the parametric equation of the curve in three dimensional space is given by ,…

Q: (i) = 5. If r(t) = tcostī + tsintī+3tk, Answer each of the following: Find an equation of the…

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

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Q: b) For a general curve r: 1R, define the vectors t(s), n(s) and b(s) as t(s) - r(s) (s) and b(s) =…

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