9- The unit tangent vector T(t) = (- sin ti + cos tj+3k) is given. Using definition of unit normal vector N = , calculate binormal vector B= T × N for the curve at t=n. |T'|

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: (c) Find dy/dx at t = T/3. (d) Include in sketch for (a) the tangent line to the curve at t = T/3…

A: We have to find the equation of tangent line.

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: Find the unit vector in the direction in which f (x,y) =x+ sin(x + 2 ·y) increases most rapidly at…

A: Given: The given function is fx,y=x+sin(x+2y) at P(0,0).

Q: Consider a water tank that is being filled with rainfall at the top and is drained through a small…

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Q: A parametric curve C is given by the position vector F(1)=sin(21). sin" (+),e' osis Osis". a) Find…

A: a)The given position vector is, r→(t)=12sin(2t),sin2t,et

Q: ü=i- where Use directional derivative definition to find Df (2.1) for the unit vector f(x y) = xy +1

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Q: What is the unit tangent vector to the curve r(t)=⟨cost, sint, et⟩ at the point where t=0?

A: Given:          r(t)=cost,sint,et at t=0           r→(0)=cos(0),sin(0),e0          r→(0)=1,0,1…

Q: Prove that the tangent vector is always orthogonal tothe position vector for the vector-valued…

A: Given r(t) =⟨sin t, sint cos t, cos2 t⟩.  we need to prove that the tangent vector is always…

Q: 3. (a) Given the vector valued function r(t) = 4cos nti + 4 sin ntj + tk. Find the position vector,…

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Q: Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 –…

A: The complete solutions are given below

Q: The unit tangent I already found which was correct was (32 , 24t , 9t^2 )*1/41 I need the…

A: To find unit normal vector

Q: Let a,,a,,a,, be positive real numb respectively, the arithmetic mean, geometr for the geometric…

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Q: |Let g(s) = e°(s4 + 6). a) Find the equation of the tangent line to g at (0, 6). y = b) Find the…

A: Differentiate at given value and then use formula of tangent and normal line

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: Let C be a curve defined by some vector function R with unit binormal B such that R(0) = (-2, 5, 4)…

A: Given C1 is a curve defined by some vector function R→ with unit binormal B→ such that R→(0)=-2,5,4,…

Q: Sketch and describe the curve defined by the vector-valued function below. 7(t) = (t cos t, t, tsin…

A: To sketch: The curve r(t)→=<tcost,t,tsint> Solution: Given x=tcost,y=t,z=tsint…

Q: A particle travels along the curve r(t) = (cos t, sin t, In(cos t)). a) Find the distance the…

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Q: r(t) = (4+t)i+(9+ln(cos t))k, -pi/2 < t < pi/2 Find principal unit  normal vector N for the curve…

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Q: for the curve defined by =(t) = (e¹, 6t, e) ind the unit tangent vector, unit normal vector, normal…

A: We know that u.v'=u'v+vu' . And if a→=&lt;a1,a2,a3&gt; then a→=a12+a22+a32 .

Q: 3. Find the unique sequence (an) of real numbers with Σk-0 akan-k = 1 for all n ≥ 0.

A:

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.