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Chapter 11: Q.49 (page 860)

Show that the graph of the vector function $r (t) = ⟨ 3 \sin t, 5 \cos t, 4 \sin t ⟩$ is a circle. (Hint: Show that the graph lies on a sphere and in a plane.)

Short Answer

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Step by step solution

Step 1. Given information.

given,

$r (t) = ⟨ 3 \sin t, 5 \cos t, 4 \sin t ⟩$

Step 2.

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Most popular questions from this chapter

In Exercises 19–21 sketch the graph of a vector-valued function $r (t) = (x (t), y (t))$ with the specified properties. Be sure to indicate the direction of increasing values oft.

Domainlocalid="1649578783745" $t \geq 0, r (0) = (1, 0), r (2) = (0, - 1), \lim_{t \to \infty} x (t) = - 2, and \lim_{t \to \infty} y (t) = - 3 .$

Evaluate the limits in Exercises 42–45.

$\underset{t \to 0}{l i m} (\sin 3 t, \cos 3 t)$

Prove that the tangent vector is always orthogonal to the position vector for the vector-valued function.

$r (t) = <\sin t, \sin t \cos t, \cos^{2} t>$

Under what conditions does a twice-differentiable vector valued function $r (t)$ not have a binormal vector at a point in the domain of $r (t)$ ?

Compute the cross product of the vector functions $r_{1} (t) = (x_{1} (t), y_{1} (t)) and (r_{2} (t) = x_{2} (t), y_{2} (t))$ by thinking of $ℝ^{2}$ as the xy-plane in $ℝ^{3} .$ That is, let $r_{1} (t) = (x_{1} (t), y_{1} (t), 0) and r_{2} (t) = (x_{2} (t), y_{2} (t), 0),$ and take the cross product of these vector functions.

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Show that the graph of the vector function $r (t) = ⟨ 3 \sin t, 5 \cos t, 4 \sin t ⟩$ is a circle. (Hint: Show that the graph lies on a sphere and in a plane.)

Short Answer

Step by step solution

Step 1. Given information.

Step 2.

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Show that the graph of the vector function r(t)=⟨3sin⁡t,5cos⁡t,4sin⁡t⟩is a circle. (Hint: Show that the graph lies on a sphere and in a plane.)

Short Answer

Step by step solution

Step 1. Given information.

Step 2.

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Mechanics Maths

Applied Mathematics

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Geometry

Study anywhere. Anytime. Across all devices.

Show that the graph of the vector function $r (t) = ⟨ 3 \sin t, 5 \cos t, 4 \sin t ⟩$ is a circle. (Hint: Show that the graph lies on a sphere and in a plane.)