Let r(t)=cos 2t i +sin 2t j + t k be a vector function. Which of the followings are true for this function? 1. Tangent vector is constant at any point. II. Length of tangent vector at any point is constant. II. Tangent vector is (0,2,1> at the point (1,0,0). 4a+b IV. Curvature at a point (a, b, c) is- 5c V. Arclength of the curve from a point (a, b, c) to a point (d, e, fl is given by /5dt O a. II, II, IV O b., II, V O.I, II,IV O d.l, I, V

Let r(t)=cos 2t i +sin 2t j + t k be a vector function. Which of the followings are true for this function? 1. Tangent vector is constant at any point. II. Length of tangent vector at any point is constant. II. Tangent vector is (0,2,1> at the point (1,0,0). 4a+b IV. Curvature at a point (a, b, c) is- 5c V. Arclength of the curve from a point (a, b, c) to a point (d, e, fl is given by /5dt O a. II, II, IV O b., II, V O.I, II,IV O d.l, I, V

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

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.

Question

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Let
r(t)=cos 2ti +sin 2t j +tk
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.
II. Tangent vector is (0,2,1) at the point (1,0,0).
4a +b
IV. Curvature at a point (a, b, c) is
50
V. Arclength of the curve from a point (a, b, c) to a point (d, e, f) is given by
O a. II, II, IV
O b. II, II, V
OC.I, II, IV
O d.I, II, V

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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. II. Tangent vector is (0,2,1) at the point (1,0,0). IV. Curvature at a point (a, b, 4а+b c) is 50 V. Arclength of the curve from a point (a, b, c) to a point (d, e, f) is given by V5dt O a. II, II, IV Ob. II, II, V O C. I, II, V Od.I, II, IV