WHICH ANSWER IS CORRECT? Given the curve C parametrized by the vector equation r⃗ (t)=3sin(t)i^+[2−sin(t)+cos(t)]j^−3cos(t)k^,t∈[0;2π] The given curve C has the property that A. Its tangent vector and acceleration vector are always orthogonal. B. The cross product between the tangent vector the acceleration vector always equals −3i^+9j^−3k^. C. The cross product of its acceleration vector and its tangent vector is always parallel to i^+3j^+k^. D. Its vector function is nowhere orthogonal to its tangent vector. E. None of the listed alternatives.

WHICH ANSWER IS CORRECT? Given the curve C parametrized by the vector equation r⃗ (t)=3sin(t)i^+[2−sin(t)+cos(t)]j^−3cos(t)k^,t∈[0;2π] The given curve C has the property that A. Its tangent vector and acceleration vector are always orthogonal. B. The cross product between the tangent vector the acceleration vector always equals −3i^+9j^−3k^. C. The cross product of its acceleration vector and its tangent vector is always parallel to i^+3j^+k^. D. Its vector function is nowhere orthogonal to its tangent vector. E. None of the listed alternatives.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.5: Polar Coordinates

Problem 97E

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WHICH ANSWER IS CORRECT?

Given the curve C parametrized by the vector equation

r⃗ (t)=3sin(t)i^+[2−sin(t)+cos(t)]j^−3cos(t)k^,t∈[0;2π]

The given curve C has the property that

A. Its tangent vector and acceleration vector are always orthogonal.

B. The cross product between the tangent vector the acceleration vector always equals

−3i^+9j^−3k^.

C. The cross product of its acceleration vector and its tangent vector is always parallel to

i^+3j^+k^.

D. Its vector function is nowhere orthogonal to its tangent vector.

E. None of the listed alternatives.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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