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1. Suppose that the last three digits of your student number are . abc . It is not important whether it is a 4 digit number or a 5 digit number, take the last three digits asabc. Let F(t) = (ta+1,tb+1,tc+1) be the given vector function. Find the following ift = 1. i. Distance from the origin r(t) = |F(t)| =? Velocityī (t) =? Speedv(t) =? ii. ii.

1. Suppose that the last three digits of your student number are . abc . It is not important whether it is a 4 digit number or a 5 digit number, take the last three digits asabc. Let F(t) = (ta+1,tb+1,tc+1) be the given vector function. Find the following ift = 1. i. Distance from the origin r(t) = |F(t)| =? Velocityī (t) =? Speedv(t) =? ii. ii.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 48E
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student ID : 000011351 (you will need this for doing the task)

1. Suppose that the last three digits of your student number are . abc . It is not important whether it is a 4 digit number or a 5 digit number, take the last three digits asabc. Let ī(t) = (ta+1, tb+1, to+1) be the given vector function. Find the following ift = 1. i. Distance from the origin r(t) = |F(t)| =? Velocityī(t) =? iii. ii. Speedv(t) =? Accelerationā(t) =? Jerkſ(t) =? Unit Tangent vectorT(t) =? Principal Unit Normal vectorN(t) =? Binomial vectorB(t) =? Curvaturek(t) =? Torsiont(t) =? Tangential component of the acceleration vector a, (t) =? iv. V. vi. vii. viii. (at least two methods) (at least two methods) ix. х. хі. (At least three methods) Tangential component of a(t) as a vector Normal component of the acceleration vector ay (t) =? Normal component of a(t) as a vector Radius of the osculating circle p(t) =? Center of the osculating circle (?,?,?) = Equation of the Normal plane (in the form Ax + By + Cz = D) Equation of the Osculating plane (in the form Ax + By + Cz = D) Equation of the Rectifying plane (in the form Ax + By + Cz = D) Equation of the Tangent line of the curve (in parametric form and in the form xii. xiii. хiv. XV. xvi. xvii. xviii. хіх. XX. y=Yo 1-Z0 = t) a (Please, find the answers in whatever order you prefer but write here in the given order, otherwise I will not check your solution. If you want to skip any of the items then make it clear that you skipped it) For example, your professor's ID number is 0000005121. So, he will study vector function F(t) = (t'+1, t2+1, ti+1) = (t²,t³, t²) att = 1.
Transcribed Image Text:1. Suppose that the last three digits of your student number are . abc . It is not important whether it is a 4 digit number or a 5 digit number, take the last three digits asabc. Let ī(t) = (ta+1, tb+1, to+1) be the given vector function. Find the following ift = 1. i. Distance from the origin r(t) = |F(t)| =? Velocityī(t) =? iii. ii. Speedv(t) =? Accelerationā(t) =? Jerkſ(t) =? Unit Tangent vectorT(t) =? Principal Unit Normal vectorN(t) =? Binomial vectorB(t) =? Curvaturek(t) =? Torsiont(t) =? Tangential component of the acceleration vector a, (t) =? iv. V. vi. vii. viii. (at least two methods) (at least two methods) ix. х. хі. (At least three methods) Tangential component of a(t) as a vector Normal component of the acceleration vector ay (t) =? Normal component of a(t) as a vector Radius of the osculating circle p(t) =? Center of the osculating circle (?,?,?) = Equation of the Normal plane (in the form Ax + By + Cz = D) Equation of the Osculating plane (in the form Ax + By + Cz = D) Equation of the Rectifying plane (in the form Ax + By + Cz = D) Equation of the Tangent line of the curve (in parametric form and in the form xii. xiii. хiv. XV. xvi. xvii. xviii. хіх. XX. y=Yo 1-Z0 = t) a (Please, find the answers in whatever order you prefer but write here in the given order, otherwise I will not check your solution. If you want to skip any of the items then make it clear that you skipped it) For example, your professor's ID number is 0000005121. So, he will study vector function F(t) = (t'+1, t2+1, ti+1) = (t²,t³, t²) att = 1.
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