Let r(t)=cos 2t i +sin 2t j + t k be a vector function. Which of the followings are true for this function? I. Tangent vector is constant at any point. II. Length of tangent vector at any point is constant. I. Tangent vector is (0,2,1) at the point (1,0,0). IV. Curvature at a point (a, b, 4a +b c) is 50 V. Arclength of the curve from a point (a, b, c) to a point (d, e, f) is given by SV5dt

Q: 2. C. b. Let (t)= and (u) = At what point P do these two space curves intersect. a. Find the tangent…

A: As per rule I need to solve only first three subparts.

Q: 2. Given r(t) = (31²,1³,-1²) find the following using vector operations. a) the unit tangent vector…

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Q: Write a formula for curvature in terms r1(t) and t1(t)

A: The rate of change of direction of the curve with respect to the distance along the curve is defined…

Q: Please sovle the following calc 3 problem and show all work by hand (explain answer)

A: Step 1: Given is the vector function below: r(t)=(8−2t)i+(2t−8)j+(7+t)k Step 2: The unit tangent…

Q: Consider the following vector function. r(t) = (2√/2t,6²², 6-2t) (a) Find the unit tangent and unit…

A: Given:  The vector function:  rt = 22t, e2t, e-2t To find: Unit tangent and unit normal vectors.

Q: Find the curvature for a circle of radius a > 0, centered at the origin, and traced cut by the…

A: Explained below

Q: Let r(t) = (-4t¹ - 4, 4e-2t, sin(-3t)) = Find the unit tangent vector T(t) at the point t T (0) = 0.…

A: Given; r(t)=<-4t4-4, 4e-2t, sin(-3t)>.

Q: r(t) = cos(t)i + V2 sin(t)j+ cos(t)k. Find the unit tangent vector T(t), the curvature K(t), the…

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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: 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: A particle moving in the x-y plane has a position vector given by r = 3/2t²i + 2/3t³j, where r is in…

A: A particle is moving in the x-y plane has a position vector given by r=32t2i+23t3j, where r is in…

Q: Find the unit tangent vector of the given curve. r(t) = (6 sin 39t) i + (6 cos ³9t)j O A. T(t) = (6…

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Q: Use the definitions to compute the unit binormal vector and torsion of the following curve. r(t) =…

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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.