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: Assume: (1) FIT calculated by percentage method and (2) Social Security 6.2% on $118,500; Medicare…

A: Based on the wage brackets provided, let's analyze how income tax withholding is calculated for a…

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: Find the unit tangent vector of the given curve. r(t) = (7t cost-7 sin t)j + (7t sin t + 7 cost) k…

A:

Q: 6. Show that (an)neN C R is bounded if and only if lim supn→∞ an < +∞o.

A: To Prove:  ann is bounded sequence if and only if limsupan&lt;+∞.

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,…

A:

Q: For the curve defined by F(t) = (e¯', 4t, e') find the unit tangent vector, unit normal vector,…

A:

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: 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 13 20 x 20+ y = 2 be the equation of a curve in the xy-plane. Find the equation y = T(x) of the…

A:

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)→=&lt;tcost,t,tsint&gt; 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…

A:

Q: Sketch a closed curve on a sheet of paper and draw a unit tangent vector T on the curve pointing in…

A:

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;…

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.