2 3. (a) At any point of the curve x = t, y = t², z = t³. Find the unit tangent vector and unit normal vector. (b) If V A = 0, V.B=0, Vx Ā 8² B Ət² equation = c²²B -10B с дt 1 V x B= -10Ä c Ət Show that B satisfy the wave

Q: 2. Find T, N the unit bi-normal vector B, and k at the given t value. (2b) r(t) = ( cost, sint, In…

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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: 5. Let 0 be the angle between vectors ū = (1,3) and i = (5, 2). What is cos 0 and what is sin 0?

A: Angle between two vectors is given by,

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A: The given curve is y=2x33 at the point 2,163. Calculate the unit vector that are parallel tot he…

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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: Determine if the derivative of the vector-valued function exists at the specified point. (Your…

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Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

A: The given vector is r→t=5t sint + 5costi^+5t cost + 5sintj^. To find: (a) unit tangent curve of the…

Q: Ifr(t) = (sin t , cos t, 29- t), then determine a vector that is perpendicular to both unit tangent…

A: Given: r(t) = sin t, cos t, 29-t To determine: A vector that is perpendicular to both unit tangent…

Q: Ans. (5) Given position vector r(t) = (t₁ t - sint, 1- cast) ⇒ r (t) = ti + (t-sint) 3 + (1 - cost)…

A: Ans. (5) Given position vector

Q: 3. Use grad h(-3,4)=5ī +3j and h(-3,4)=10 to answer the following questions. a) Find the…

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Q: Find the tangential and normal components of acceleration for the positio denoted by ř = (cos 2t,–…

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Q: Find the positive t when the vector r(t) = (4t, 4t, 5t2 – 6) is perpendicular to r' (t). t =

A: We use the definition of the perpendicular of two vectors to find the positive value of t.

Q: Find a vector parametric equation F(t) for the line through the points P = (1,0,-5) and Q=(2,3,-7)…

A: The vector parametric equation of the line that passes through the points: A=x1, y1, z1, B=x2, y2,…

Q: e vector equation ū=

A:

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: 1) A point moves along a circle with position vector given by r(t) = a) Write a (t) as a combination…

A: Since you have posted a multi subparts question according to guidelines I will solve first…

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

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Q: 2. Let 7(t) = (1, tv2, In(t)). (a) Find 7"(t). (b) Find 7(t) and simplify completely. (c) Find the…

A: Given, r→t=12t2, t2, lnt Used differentiation formulas, ddxxn=nxn-1ddxlnx=1xddxCfx=Cddxfx    C is…

Q: Find the tangential and normal components

A: Given,

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A: Given, r→=i^(2cos2t)+j^(2sin2t) Identify the direction vector, From the given position vector,…

Q: On a metal plate in the shape of a rectangle, the temperature at a point (x,y) is given by; 100 3x²…

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Q: Part B please g(x,y,z)=x^2+y^2+(z-3)^2

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Q: Find Components of the Acceleration For the curve defined by T(t) = (e-t cos(t), e' sin(t)) |3D find…

A: To find- For the curve defined by r→t = e-tcost, et sint, find the unit tangent vector, unit normal…

Q: 1. Let ř(t) = (In |t – 1|, e', vi ) (a) Express the vector valued function in parametric form. (b)…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: = 27. If f(x, y) = −3x² + 4y², find the value of the directional derivative at the point (1, -1) in…

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Q: A point moving a long a curve whose position vector is R(t)=(t sin t +cost)i+(sin t-t cost)j+4 k;…

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Q: 4. Consider r(t) = (cos(3t), sin(3t), 4t), the curve from #2. Find the principal unit normal vector…

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